%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:20 AM UTC 2026
% Result : Theorem 11.86s 2.42s
% Output : CNFRefutation 11.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 89
% Syntax : Number of formulae : 1347 ( 479 unt; 0 typ; 0 def)
% Number of atoms : 8429 (4144 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 13036 (2985 ~;2449 |; 24 &;7407 @)
% ( 0 <=>; 171 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 312 ( 312 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 6 con; 0-3 aty)
% Number of variables : 2759 ( 4 ^;2728 !; 27 ?;2759 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_int,type,
int: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_polyno727731844poly_a,type,
polyno727731844poly_a: $tType ).
thf(tp_minus_minus_int,type,
minus_minus_int: int > int > int ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(tp_n,type,
n: nat ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_p,type,
p: polyno727731844poly_a ).
thf(tp_polyno1372495879olyh_a,type,
polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
thf(tp_polyno1674775833reen_a,type,
polyno1674775833reen_a: polyno727731844poly_a > nat > nat ).
thf(tp_polyno190918219poly_a,type,
polyno190918219poly_a: polyno727731844poly_a > $o ).
thf(tp_polyno578545843gree_a,type,
polyno578545843gree_a: polyno727731844poly_a > nat ).
thf(tp_power_power_int,type,
power_power_int: int > nat > int ).
thf(tp_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(tp_sK10_SY202,type,
sK10_SY202: nat > ( nat > $o ) > nat ).
thf(tp_sK11_SY195,type,
sK11_SY195: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK12_SY191,type,
sK12_SY191: nat > nat ).
thf(tp_sK13_SY215,type,
sK13_SY215: ( nat > $o ) > nat > nat ).
thf(tp_sK14_SY188,type,
sK14_SY188: nat > ( nat > $o ) > nat ).
thf(tp_sK15_SY209,type,
sK15_SY209: nat > nat > nat ).
thf(tp_sK16_SY211,type,
sK16_SY211: ( nat > $o ) > nat > nat ).
thf(tp_sK17_SY196,type,
sK17_SY196: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK18_SY209,type,
sK18_SY209: nat > nat > nat ).
thf(tp_sK19_SY212,type,
sK19_SY212: ( nat > $o ) > nat > nat ).
thf(tp_sK1_SY149,type,
sK1_SY149: nat > nat ).
thf(tp_sK20_SY191,type,
sK20_SY191: nat > nat > nat ).
thf(tp_sK21_SY231,type,
sK21_SY231: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK22_SY211,type,
sK22_SY211: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK23_SY212,type,
sK23_SY212: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK24_SY211,type,
sK24_SY211: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK25_SY209,type,
sK25_SY209: nat > nat > nat > nat ).
thf(tp_sK26_SY212,type,
sK26_SY212: nat > ( nat > $o ) > nat > nat ).
thf(tp_sK2_SY157,type,
sK2_SY157: nat > nat ).
thf(tp_sK3_SY168,type,
sK3_SY168: nat > nat ).
thf(tp_sK4_SY190,type,
sK4_SY190: nat > nat ).
thf(tp_sK5_SY194,type,
sK5_SY194: nat > nat > ( nat > nat > $o ) > nat ).
thf(tp_sK6_SY155,type,
sK6_SY155: nat > ( nat > $o ) > nat ).
thf(tp_sK7_SY165,type,
sK7_SY165: nat > ( nat > $o ) > nat ).
thf(tp_sK8_SY214,type,
sK8_SY214: ( nat > $o ) > nat > nat ).
thf(tp_sK9_SY183,type,
sK9_SY183: nat > ( nat > $o ) > nat ).
thf(tp_semiri1382578993at_nat,type,
semiri1382578993at_nat: nat > nat ).
thf(tp_semiri2019852685at_int,type,
semiri2019852685at_int: nat > int ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_zero_zero_int,type,
zero_zero_int: int ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(11,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_le__numeral__extra_I3_J) ).
thf(12,axiom,
! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_zero__le) ).
thf(19,axiom,
! [N: nat,A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( power_power_nat @ A @ N )
= ( power_power_nat @ B @ N ) )
= ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_power__eq__iff__eq__base) ).
thf(21,axiom,
! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ N )
= ( power_power_nat @ B @ N ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_power__eq__imp__eq__base) ).
thf(22,axiom,
! [I: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_nat__one__le__power) ).
thf(34,axiom,
! [A: nat,B: nat,N: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_power__mono) ).
thf(37,axiom,
! [A: nat,N: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_zero__le__power) ).
thf(43,axiom,
! [A: nat,N: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_power__less__imp__less__base) ).
thf(44,axiom,
! [A: nat,N: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_power__not__zero) ).
thf(104,axiom,
! [A: nat,N: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_power__le__imp__le__base) ).
thf(108,axiom,
! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ ( suc @ N ) )
= ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_power__inject__base) ).
thf(120,axiom,
! [A: nat,B: nat,N: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
= ( ord_less_eq_nat @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_power__mono__iff) ).
thf(125,axiom,
! [A: nat,N: nat] :
( ( ( power_power_nat @ A @ N )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_power__eq__0__iff) ).
thf(126,axiom,
! [A: int,N: nat] :
( ( ( power_power_int @ A @ N )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_power__eq__0__iff) ).
thf(127,axiom,
! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_zero__less__diff) ).
thf(128,axiom,
! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_power__Suc0__right) ).
thf(133,axiom,
! [N: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_power__0__Suc) ).
thf(139,axiom,
! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_diff__0__eq__0) ).
thf(140,axiom,
! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_diff__self__eq__0) ).
thf(141,axiom,
! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_diff__is__0__eq) ).
thf(142,axiom,
! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_diff__is__0__eq_H) ).
thf(143,axiom,
! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_nat__zero__less__power__iff) ).
thf(150,axiom,
! [N: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_power__Suc__0) ).
thf(151,axiom,
! [X: nat,M: nat] :
( ( ( power_power_nat @ X @ M )
= ( suc @ zero_zero_nat ) )
= ( ( M = zero_zero_nat )
| ( X
= ( suc @ zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_nat__power__eq__Suc__0__iff) ).
thf(156,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_zero__diff) ).
thf(157,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_diff__zero) ).
thf(159,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(161,axiom,
! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_le__zero__eq) ).
thf(164,axiom,
! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_le0) ).
thf(165,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_bot__nat__0_Oextremum) ).
thf(168,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Suc__pred) ).
thf(169,axiom,
! [M: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_of__nat__le__0__iff) ).
thf(170,axiom,
! [M: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_of__nat__le__0__iff) ).
thf(172,axiom,
! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ X ) @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_of__nat__zero__less__power__iff) ).
thf(173,axiom,
! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_12: nat] : ( P @ X_12 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_exists__least__lemma) ).
thf(247,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_less__Suc__eq__0__disj) ).
thf(248,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_gr0__implies__Suc) ).
thf(249,axiom,
! [N: nat,P: nat > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
=> ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ N )
=> ( P @ ( suc @ I2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_All__less__Suc2) ).
thf(250,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_gr0__conv__Suc) ).
thf(251,axiom,
! [N: nat,P: nat > $o] :
( ( ? [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
& ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I2: nat] :
( ( ord_less_nat @ I2 @ N )
& ( P @ ( suc @ I2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Ex__less__Suc2) ).
thf(261,axiom,
! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_of__nat__less__0__iff) ).
thf(279,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_not0__implies__Suc) ).
thf(280,axiom,
! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_old_Onat_Oinducts) ).
thf(281,axiom,
! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_old_Onat_Oexhaust) ).
thf(282,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Zero__not__Suc) ).
thf(283,axiom,
! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Zero__neq__Suc) ).
thf(284,axiom,
! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Suc__neq__Zero) ).
thf(285,axiom,
! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zero__induct) ).
thf(286,axiom,
! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_diff__induct) ).
thf(287,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__induct) ).
thf(288,axiom,
! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_nat_OdiscI) ).
thf(289,axiom,
! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_old_Onat_Odistinct_I1_J) ).
thf(290,axiom,
! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_old_Onat_Odistinct_I2_J) ).
thf(291,axiom,
! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nat_Odistinct_I1_J) ).
thf(292,axiom,
! [X: nat] :
( ( X != zero_zero_nat )
=> ~ ! [V: nat] :
( X
!= ( suc @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_polypow_Ocases) ).
thf(294,axiom,
! [N: nat] :
( ( semiri1382578993at_nat @ ( suc @ N ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_of__nat__neq__0) ).
thf(297,axiom,
! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zero__less__Suc) ).
thf(298,axiom,
! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__Suc0) ).
thf(301,axiom,
! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_of__nat__eq__0__iff) ).
thf(302,axiom,
! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__nat__eq__0__iff) ).
thf(303,axiom,
! [N: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N ) )
= ( zero_zero_nat = N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_of__nat__0__eq__iff) ).
thf(304,axiom,
! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_of__nat__0__eq__iff) ).
thf(305,axiom,
( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_of__nat__0) ).
thf(306,axiom,
( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_of__nat__0) ).
thf(316,axiom,
zero_zero_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__natural_Orsp) ).
thf(317,axiom,
! [P3: polyno727731844poly_a,N: nat] :
( ( polyno1372495879olyh_a @ P3 @ ( suc @ N ) )
=> ( ( polyno578545843gree_a @ P3 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_degree__isnpolyh__Suc) ).
thf(319,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_of__nat__0__less__iff) ).
thf(320,axiom,
! [P3: polyno727731844poly_a,N: nat,M: nat] :
( ( polyno1372495879olyh_a @ P3 @ N )
=> ( ( ord_less_nat @ M @ N )
=> ( ( polyno1674775833reen_a @ P3 @ M )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_degreen__0) ).
thf(321,axiom,
( polyno190918219poly_a
= ( ^ [P2: polyno727731844poly_a] : ( polyno1372495879olyh_a @ P2 @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_isnpoly__def) ).
thf(323,axiom,
~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_less__numeral__extra_I3_J) ).
thf(324,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_gr__zeroI) ).
thf(325,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_not__less__zero) ).
thf(326,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_gr__implies__not__zero) ).
thf(327,axiom,
! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_zero__less__iff__neq__zero) ).
thf(337,axiom,
! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__reorient) ).
thf(338,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_bot__nat__0_Oextremum__strict) ).
thf(339,axiom,
! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_infinite__descent0) ).
thf(340,axiom,
! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_gr__implies__not0) ).
thf(341,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__zeroE) ).
thf(342,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_not__less0) ).
thf(343,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__gr0) ).
thf(344,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_gr0I) ).
thf(345,axiom,
! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_not__gr__zero) ).
thf(346,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bot__nat__0_Onot__eq__extremum) ).
thf(347,axiom,
! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_less__nat__zero__code) ).
thf(348,axiom,
! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_neq0__conv) ).
thf(349,axiom,
polyno1372495879olyh_a @ p @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(350,axiom,
ord_less_nat @ zero_zero_nat @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(351,conjecture,
( ( polyno578545843gree_a @ p )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(352,negated_conjecture,
( ( ( polyno578545843gree_a @ p )
= zero_zero_nat )
= $false ),
inference(negate_conjecture,[status(cth)],[351]) ).
thf(353,plain,
( ( ( polyno578545843gree_a @ p )
= zero_zero_nat )
= $false ),
inference(unfold_def,[status(thm)],[352]) ).
thf(354,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(355,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(356,plain,
( ( ! [N: nat,A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( power_power_nat @ A @ N )
= ( power_power_nat @ B @ N ) )
= ( A = B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(357,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ N )
= ( power_power_nat @ B @ N ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( A = B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(358,plain,
( ( ! [I: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(359,plain,
( ( ! [A: nat,B: nat,N: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(360,plain,
( ( ! [A: nat,N: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(361,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(362,plain,
( ( ! [A: nat,N: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(363,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(364,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ ( suc @ N ) )
= ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(365,plain,
( ( ! [A: nat,B: nat,N: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
= ( ord_less_eq_nat @ A @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(366,plain,
( ( ! [A: nat,N: nat] :
( ( ( power_power_nat @ A @ N )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(367,plain,
( ( ! [A: int,N: nat] :
( ( ( power_power_int @ A @ N )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(368,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(369,plain,
( ( ! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(370,plain,
( ( ! [N: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(371,plain,
( ( ! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(372,plain,
( ( ! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(373,plain,
( ( ! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(374,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(375,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(376,plain,
( ( ! [N: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
= ( suc @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(377,plain,
( ( ! [X: nat,M: nat] :
( ( ( power_power_nat @ X @ M )
= ( suc @ zero_zero_nat ) )
= ( ( M = zero_zero_nat )
| ( X
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(378,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(379,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(380,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(381,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(382,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(383,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(384,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(385,plain,
( ( ! [M: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(386,plain,
( ( ! [M: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(387,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ X ) @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(388,plain,
( ( ! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_12: nat] : ( P @ X_12 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(389,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(390,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(391,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
=> ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ N )
=> ( P @ ( suc @ I2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(392,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(393,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
& ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I2: nat] :
( ( ord_less_nat @ I2 @ N )
& ( P @ ( suc @ I2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(394,plain,
( ( ! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(395,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(396,plain,
( ( ! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(397,plain,
( ( ! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(398,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(399,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(400,plain,
( ( ! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(401,plain,
( ( ! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(402,plain,
( ( ! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(403,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(404,plain,
( ( ! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(405,plain,
( ( ! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(406,plain,
( ( ! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(407,plain,
( ( ! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(408,plain,
( ( ! [X: nat] :
( ( X != zero_zero_nat )
=> ~ ! [V: nat] :
( X
!= ( suc @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(409,plain,
( ( ! [N: nat] :
( ( semiri1382578993at_nat @ ( suc @ N ) )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(410,plain,
( ( ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(411,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(412,plain,
( ( ! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(413,plain,
( ( ! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(414,plain,
( ( ! [N: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(415,plain,
( ( ! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(416,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(417,plain,
( ( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(418,plain,
( ( zero_zero_nat = zero_zero_nat )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(419,plain,
( ( ! [P3: polyno727731844poly_a,N: nat] :
( ( polyno1372495879olyh_a @ P3 @ ( suc @ N ) )
=> ( ( polyno578545843gree_a @ P3 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(420,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(421,plain,
( ( ! [P3: polyno727731844poly_a,N: nat,M: nat] :
( ( polyno1372495879olyh_a @ P3 @ N )
=> ( ( ord_less_nat @ M @ N )
=> ( ( polyno1674775833reen_a @ P3 @ M )
= zero_zero_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(422,plain,
( ( polyno190918219poly_a
= ( ^ [P2: polyno727731844poly_a] : ( polyno1372495879olyh_a @ P2 @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(423,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(424,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(425,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(426,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(427,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(428,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(429,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(430,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(431,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(432,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(433,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(434,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(435,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(436,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(437,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(438,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(439,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(440,plain,
( ( polyno1372495879olyh_a @ p @ n )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(441,plain,
( ( ord_less_nat @ zero_zero_nat @ n )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(442,plain,
( ( ( polyno578545843gree_a @ p )
!= zero_zero_nat )
= $true ),
inference(polarity_switch,[status(thm)],[353]) ).
thf(443,plain,
( ( ord_less_nat @ zero_zero_nat @ n )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(444,plain,
( ( polyno1372495879olyh_a @ p @ n )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(445,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(446,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(447,plain,
( ( ! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(448,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(449,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(450,plain,
( ( ! [N: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(451,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(452,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(453,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(454,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( ord_less_nat @ zero_zero_nat @ N2 )
=> ( ~ ( P @ N2 )
=> ? [M2: nat] :
( ( ord_less_nat @ M2 @ N2 )
& ~ ( P @ M2 ) ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(455,plain,
( ( ! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(456,plain,
( ( ! [X: nat] :
( ( zero_zero_nat = X )
= ( X = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(457,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(458,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ N )
=> ( N != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(459,plain,
( ( ! [N: nat] :
~ ( ord_less_nat @ N @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(460,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(461,plain,
( ( ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(462,plain,
( ( polyno190918219poly_a
= ( ^ [P2: polyno727731844poly_a] : ( polyno1372495879olyh_a @ P2 @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(463,plain,
( ( ! [P3: polyno727731844poly_a,N: nat,M: nat] :
( ( polyno1372495879olyh_a @ P3 @ N )
=> ( ( ord_less_nat @ M @ N )
=> ( ( polyno1674775833reen_a @ P3 @ M )
= zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(464,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
= ( ord_less_nat @ zero_zero_nat @ N ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(465,plain,
( ( ! [P3: polyno727731844poly_a,N: nat] :
( ( polyno1372495879olyh_a @ P3 @ ( suc @ N ) )
=> ( ( polyno578545843gree_a @ P3 )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(466,plain,
( ( zero_zero_nat = zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(467,plain,
( ( ( semiri1382578993at_nat @ zero_zero_nat )
= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(468,plain,
( ( ( semiri2019852685at_int @ zero_zero_nat )
= zero_zero_int )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(469,plain,
( ( ! [N: nat] :
( ( zero_zero_nat
= ( semiri1382578993at_nat @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(470,plain,
( ( ! [N: nat] :
( ( zero_zero_int
= ( semiri2019852685at_int @ N ) )
= ( zero_zero_nat = N ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(471,plain,
( ( ! [M: nat] :
( ( ( semiri1382578993at_nat @ M )
= zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(472,plain,
( ( ! [M: nat] :
( ( ( semiri2019852685at_int @ M )
= zero_zero_int )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(473,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(474,plain,
( ( ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(475,plain,
( ( ! [N: nat] :
( ( semiri1382578993at_nat @ ( suc @ N ) )
!= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(476,plain,
( ( ! [X: nat] :
( ( X != zero_zero_nat )
=> ~ ! [V: nat] :
( X
!= ( suc @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(477,plain,
( ( ! [X2: nat] :
( zero_zero_nat
!= ( suc @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(478,plain,
( ( ! [Nat2: nat] :
( ( suc @ Nat2 )
!= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(479,plain,
( ( ! [Nat2: nat] :
( zero_zero_nat
!= ( suc @ Nat2 ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(480,plain,
( ( ! [Nat: nat,X2: nat] :
( ( Nat
= ( suc @ X2 ) )
=> ( Nat != zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(481,plain,
( ( ! [P: nat > $o,N: nat] :
( ( P @ zero_zero_nat )
=> ( ! [N2: nat] :
( ( P @ N2 )
=> ( P @ ( suc @ N2 ) ) )
=> ( P @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(482,plain,
( ( ! [P: nat > nat > $o,M: nat,N: nat] :
( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
=> ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
=> ( ! [X3: nat,Y3: nat] :
( ( P @ X3 @ Y3 )
=> ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
=> ( P @ M @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(483,plain,
( ( ! [P: nat > $o,K: nat] :
( ( P @ K )
=> ( ! [N2: nat] :
( ( P @ ( suc @ N2 ) )
=> ( P @ N2 ) )
=> ( P @ zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(484,plain,
( ( ! [M: nat] :
( ( suc @ M )
!= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(485,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(486,plain,
( ( ! [M: nat] :
( zero_zero_nat
!= ( suc @ M ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(487,plain,
( ( ! [Y: nat] :
( ( Y != zero_zero_nat )
=> ~ ! [Nat3: nat] :
( Y
!= ( suc @ Nat3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(488,plain,
( ( ! [P: nat > $o,Nat: nat] :
( ( P @ zero_zero_nat )
=> ( ! [Nat3: nat] :
( ( P @ Nat3 )
=> ( P @ ( suc @ Nat3 ) ) )
=> ( P @ Nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(489,plain,
( ( ! [N: nat] :
( ( N != zero_zero_nat )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(490,plain,
( ( ! [M: nat] :
~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(491,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ? [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
& ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
| ? [I2: nat] :
( ( ord_less_nat @ I2 @ N )
& ( P @ ( suc @ I2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(492,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
= ( ? [M5: nat] :
( N
= ( suc @ M5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(493,plain,
( ( ! [N: nat,P: nat > $o] :
( ( ! [I2: nat] :
( ( ord_less_nat @ I2 @ ( suc @ N ) )
=> ( P @ I2 ) ) )
= ( ( P @ zero_zero_nat )
& ! [I2: nat] :
( ( ord_less_nat @ I2 @ N )
=> ( P @ ( suc @ I2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(494,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ? [M3: nat] :
( N
= ( suc @ M3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(495,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_nat @ M @ ( suc @ N ) )
= ( ( M = zero_zero_nat )
| ? [J3: nat] :
( ( M
= ( suc @ J3 ) )
& ( ord_less_nat @ J3 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(496,plain,
( ( ! [P: nat > $o] :
( ~ ( P @ zero_zero_nat )
=> ( ? [X_12: nat] : ( P @ X_12 )
=> ? [N2: nat] :
( ~ ( P @ N2 )
& ( P @ ( suc @ N2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(497,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ X ) @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(498,plain,
( ( ! [M: nat] :
( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(499,plain,
( ( ! [M: nat] :
( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
= ( M = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(500,plain,
( ( ! [N: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
= N ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(501,plain,
( ( ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(502,plain,
( ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(503,plain,
( ( ! [N: nat] :
( ( ord_less_eq_nat @ N @ zero_zero_nat )
= ( N = zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(504,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(505,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(506,plain,
( ( ! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(507,plain,
( ( ! [X: nat,M: nat] :
( ( ( power_power_nat @ X @ M )
= ( suc @ zero_zero_nat ) )
= ( ( M = zero_zero_nat )
| ( X
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(508,plain,
( ( ! [N: nat] :
( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
= ( suc @ zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(509,plain,
( ( ! [X: nat,N: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
= ( ( ord_less_nat @ zero_zero_nat @ X )
| ( N = zero_zero_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(510,plain,
( ( ! [M: nat,N: nat] :
( ( ord_less_eq_nat @ M @ N )
=> ( ( minus_minus_nat @ M @ N )
= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(511,plain,
( ( ! [M: nat,N: nat] :
( ( ( minus_minus_nat @ M @ N )
= zero_zero_nat )
= ( ord_less_eq_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(512,plain,
( ( ! [M: nat] :
( ( minus_minus_nat @ M @ M )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(513,plain,
( ( ! [N: nat] :
( ( minus_minus_nat @ zero_zero_nat @ N )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(514,plain,
( ( ! [N: nat] :
( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
= zero_zero_nat ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(515,plain,
( ( ! [A: nat] :
( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(516,plain,
( ( ! [N: nat,M: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
= ( ord_less_nat @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(517,plain,
( ( ! [A: int,N: nat] :
( ( ( power_power_int @ A @ N )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(518,plain,
( ( ! [A: nat,N: nat] :
( ( ( power_power_nat @ A @ N )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ord_less_nat @ zero_zero_nat @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(519,plain,
( ( ! [A: nat,B: nat,N: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
= ( ord_less_eq_nat @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(520,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ ( suc @ N ) )
= ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( A = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(521,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(522,plain,
( ( ! [A: nat,N: nat] :
( ( A != zero_zero_nat )
=> ( ( power_power_nat @ A @ N )
!= zero_zero_nat ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(523,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_nat @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(524,plain,
( ( ! [A: nat,N: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(525,plain,
( ( ! [A: nat,B: nat,N: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(526,plain,
( ( ! [I: nat,N: nat] :
( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(527,plain,
( ( ! [A: nat,N: nat,B: nat] :
( ( ( power_power_nat @ A @ N )
= ( power_power_nat @ B @ N ) )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_nat @ zero_zero_nat @ N )
=> ( A = B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(528,plain,
( ( ! [N: nat,A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ N )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( power_power_nat @ A @ N )
= ( power_power_nat @ B @ N ) )
= ( A = B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(529,plain,
( ( ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(530,plain,
( ( ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(531,plain,
( ( ( polyno578545843gree_a @ p )
!= zero_zero_nat )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(532,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(533,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ( ( minus_minus_nat @ SX0 @ SX1 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(534,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(535,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(536,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
!= ( power_power_nat @ SX2 @ SX1 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(537,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ( ord_less_eq_nat @ ( power_power_nat @ SX0 @ SX2 ) @ ( power_power_nat @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(538,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX2 )
| ~ ~ ( SX0 @ SX2 )
| ~ ! [SX3: nat] :
~ ~ ( ~ ( ord_less_nat @ SX3 @ SX2 )
| ~ ~ ( SX0 @ SX3 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(539,plain,
( ( ! [SX0: nat] :
( ( semiri1382578993at_nat @ ( suc @ SX0 ) )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(540,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(541,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ( ( power_power_nat @ SX0 @ ( suc @ SX1 ) )
!= ( power_power_nat @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(542,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ( ( power_power_nat @ SX1 @ SX0 )
= ( power_power_nat @ SX2 @ SX0 ) )
= ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(543,plain,
( ( ! [SX0: nat] :
( ( suc @ SX0 )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(544,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(545,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(546,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ord_less_nat @ SX0 @ ( suc @ SX1 ) )
= ( ( SX0 = zero_zero_nat )
| ~ ! [SX2: nat] :
~ ~ ( ( SX0
!= ( suc @ SX2 ) )
| ~ ( ord_less_nat @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(547,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: nat] :
( ~ ( SX0 @ ( suc @ SX2 ) )
| ( SX0 @ SX2 ) )
| ( SX0 @ zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(548,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(549,plain,
( ( ! [SX0: int,SX1: nat] :
( ( ( power_power_int @ SX0 @ SX1 )
= zero_zero_int )
= ( ~ ( ( SX0 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(550,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( ( power_power_nat @ SX0 @ SX1 )
= zero_zero_nat )
= ( ~ ( ( SX0 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(551,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(552,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ ( suc @ SX0 ) )
| ~ ( SX1 @ SX2 ) ) )
= ( ( SX1 @ zero_zero_nat )
| ~ ! [SX2: nat] :
~ ~ ( ~ ( ord_less_nat @ SX2 @ SX0 )
| ~ ( SX1 @ ( suc @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(553,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(554,plain,
( ( ! [SX0: nat,SX1: nat] :
( ( SX0
!= ( suc @ SX1 ) )
| ( SX0 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(555,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SX0 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX1 )
| ~ ( ord_less_nat @ zero_zero_nat @ SX2 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SX0 @ SX2 ) @ ( power_power_nat @ SX1 @ SX2 ) )
= ( ord_less_eq_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(556,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(557,plain,
( ( ! [SX0: nat] :
( ( SX0 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(558,plain,
( ( ! [SX0: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SX0 )
| ( ( suc @ ( minus_minus_nat @ SX0 @ ( suc @ zero_zero_nat ) ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(559,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SX0 )
| ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(560,plain,
( ( ! [SX0: nat,SX1: nat > $o] :
( ( ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ ( suc @ SX0 ) )
| ( SX1 @ SX2 ) ) )
= ( ~ ( ~ ( SX1 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( ord_less_nat @ SX2 @ SX0 )
| ( SX1 @ ( suc @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(561,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(562,plain,
( ( ! [SX0: polyno727731844poly_a,SX1: nat,SX2: nat] :
( ~ ( polyno1372495879olyh_a @ SX0 @ SX1 )
| ~ ( ord_less_nat @ SX2 @ SX1 )
| ( ( polyno1674775833reen_a @ SX0 @ SX2 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(563,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( suc @ SX2 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(564,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SX0 @ SX1 ) @ ( power_power_nat @ SX2 @ SX1 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(565,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ord_less_nat @ SX0 @ SX1 )
| ( SX1 != zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(566,plain,
( ( ! [SX0: nat > $o] :
( ~ ~ ( SX0 @ zero_zero_nat )
| ~ ~ ! [SX1: nat] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: nat] :
~ ~ ( ~ ~ ( SX0 @ SX1 )
| ~ ( SX0 @ ( suc @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(567,plain,
( ( ! [SX0: nat,SX1: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ( power_power_nat @ SX0 @ SX1 )
!= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(568,plain,
( ( ! [SX0: nat] :
( zero_zero_nat
!= ( suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(569,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(570,plain,
( ( ! [SX0: nat] :
( ( ord_less_nat @ zero_zero_nat @ SX0 )
= ( ~ ! [SX1: nat] :
( SX0
!= ( suc @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(571,plain,
( ( ! [SX0: nat > nat > $o,SX1: nat,SX2: nat] :
( ~ ! [SX3: nat] : ( SX0 @ SX3 @ zero_zero_nat )
| ~ ! [SX3: nat] : ( SX0 @ zero_zero_nat @ ( suc @ SX3 ) )
| ~ ! [SX3: nat,SX4: nat] :
( ~ ( SX0 @ SX3 @ SX4 )
| ( SX0 @ ( suc @ SX3 ) @ ( suc @ SX4 ) ) )
| ( SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(572,plain,
( ( ! [SX0: nat] :
( ~ ( ( SX0 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(573,plain,
( ( ! [SX0: nat,SX1: nat,SX2: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SX0 @ ( suc @ SX1 ) ) @ ( power_power_nat @ SX2 @ ( suc @ SX1 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SX2 )
| ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(574,plain,
( ( ! [SX0: nat] :
( ( suc @ SX0 )
!= zero_zero_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(575,plain,
( ( ! [SX0: polyno727731844poly_a,SX1: nat] :
( ~ ( polyno1372495879olyh_a @ SX0 @ ( suc @ SX1 ) )
| ( ( polyno578545843gree_a @ SX0 )
= zero_zero_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(576,plain,
( ( ! [SX0: nat > $o,SX1: nat] :
( ~ ( SX0 @ zero_zero_nat )
| ~ ! [SX2: nat] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( suc @ SX2 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(577,plain,
! [SV1: nat] :
( ( ~ ( ord_less_nat @ SV1 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(578,plain,
! [SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= ( SV2 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(579,plain,
! [SV3: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= ( SV3 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(580,plain,
! [SV4: nat] :
( ( ~ ( ord_less_nat @ SV4 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(581,plain,
! [SV5: nat] :
( ( ~ ( ord_less_nat @ SV5 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(582,plain,
! [SV6: nat] :
( ( ~ ( ord_less_nat @ SV6 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(583,plain,
! [SV7: nat] :
( ( ( zero_zero_nat = SV7 )
= ( SV7 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(584,plain,
! [SV8: nat] :
( ( ~ ( ord_less_nat @ SV8 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(585,plain,
( ( ord_less_nat @ zero_zero_nat @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(586,plain,
( ( ! [SV9: polyno727731844poly_a] :
( ( polyno190918219poly_a @ SV9 )
= ( polyno1372495879olyh_a @ SV9 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[462]) ).
thf(587,plain,
( ( polyno190918219poly_a
= ( ^ [P2: polyno727731844poly_a] : ( polyno1372495879olyh_a @ P2 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[462]) ).
thf(588,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(589,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= ( zero_zero_nat = SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(590,plain,
! [SV12: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= ( zero_zero_nat = SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(591,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= ( SV13 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(592,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= ( SV14 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(593,plain,
! [SV15: nat] :
( ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= ( SV15 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(594,plain,
! [SV16: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( suc @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(595,plain,
! [SV17: nat] :
( ( ~ ( ord_less_nat @ ( semiri1382578993at_nat @ SV17 ) @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(596,plain,
! [SV18: nat] :
( ( ! [SY142: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SY142 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SY142 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(597,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= ( SV19 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(598,plain,
! [SV20: nat] :
( ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= ( SV20 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(599,plain,
! [SV21: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(600,plain,
! [SV22: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(601,plain,
! [SV23: nat] :
( ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= ( SV23 = zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(602,plain,
! [SV24: nat] :
( ( ( minus_minus_nat @ SV24 @ SV24 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(603,plain,
! [SV25: nat] :
( ( ( minus_minus_nat @ SV25 @ zero_zero_nat )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(604,plain,
! [SV26: nat] :
( ( ( minus_minus_nat @ zero_zero_nat @ SV26 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(605,plain,
! [SV27: nat] :
( ( ! [SY143: nat] :
( ( ( power_power_nat @ SV27 @ SY143 )
= ( suc @ zero_zero_nat ) )
= ( ( SY143 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(606,plain,
! [SV28: nat] :
( ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ SV28 )
= ( suc @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(607,plain,
! [SV29: nat] :
( ( ! [SY144: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SY144 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SY144 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(608,plain,
! [SV30: nat] :
( ( ! [SY145: nat] :
( ( ( minus_minus_nat @ SV30 @ SY145 )
= zero_zero_nat )
= ( ord_less_eq_nat @ SV30 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(609,plain,
! [SV31: nat] :
( ( ( minus_minus_nat @ SV31 @ SV31 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(610,plain,
! [SV32: nat] :
( ( ( minus_minus_nat @ zero_zero_nat @ SV32 )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(611,plain,
! [SV33: nat] :
( ( ( power_power_nat @ zero_zero_nat @ ( suc @ SV33 ) )
= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(612,plain,
! [SV34: nat] :
( ( ( power_power_nat @ SV34 @ ( suc @ zero_zero_nat ) )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(613,plain,
! [SV35: nat] :
( ( ! [SY146: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SY146 ) )
= ( ord_less_nat @ SY146 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(614,plain,
! [SV36: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(615,plain,
( ( ( polyno578545843gree_a @ p )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(616,plain,
! [SV37: nat] :
( ( zero_zero_nat
!= ( suc @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(617,plain,
! [SV38: nat] :
( ( ! [SY147: nat] :
( ~ ( ord_less_eq_nat @ SV38 @ SY147 )
| ( ( minus_minus_nat @ SV38 @ SY147 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(618,plain,
! [SV39: nat] :
( ( ! [SY148: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV39 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV39 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(619,plain,
! [SV40: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV40 )
| ~ ! [SY149: nat] :
( SV40
!= ( suc @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(620,plain,
! [SV41: nat] :
( ( ! [SY150: nat,SY151: nat] :
( ( ( power_power_nat @ SV41 @ SY150 )
!= ( power_power_nat @ SY151 @ SY150 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY151 )
| ~ ( ord_less_nat @ zero_zero_nat @ SY150 )
| ( SV41 = SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(621,plain,
! [SV42: nat] :
( ( ! [SY152: nat,SY153: nat] :
( ~ ( ord_less_eq_nat @ SV42 @ SY152 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV42 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SY153 ) @ ( power_power_nat @ SY152 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(622,plain,
! [SV43: nat > $o] :
( ( ! [SY154: nat] :
( ~ ( SV43 @ zero_zero_nat )
| ~ ! [SY155: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY155 )
| ~ ~ ( SV43 @ SY155 )
| ~ ! [SY156: nat] :
~ ~ ( ~ ( ord_less_nat @ SY156 @ SY155 )
| ~ ~ ( SV43 @ SY156 ) ) )
| ( SV43 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(623,plain,
! [SV44: nat] :
( ( ( semiri1382578993at_nat @ ( suc @ SV44 ) )
!= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(624,plain,
! [SV45: nat] :
( ( ~ ( ( SV45 != zero_zero_nat ) )
| ~ ! [SY157: nat] :
( SV45
!= ( suc @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(625,plain,
! [SV46: nat] :
( ( ! [SY158: nat,SY159: nat] :
( ( ( power_power_nat @ SV46 @ ( suc @ SY158 ) )
!= ( power_power_nat @ SY159 @ ( suc @ SY158 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY159 )
| ( SV46 = SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(626,plain,
! [SV47: nat] :
( ( ! [SY160: nat,SY161: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SV47 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY160 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY161 )
| ( ( ( power_power_nat @ SY160 @ SV47 )
= ( power_power_nat @ SY161 @ SV47 ) )
= ( SY160 = SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(627,plain,
! [SV48: nat] :
( ( ( suc @ SV48 )
!= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(628,plain,
! [SV49: nat] :
( ( zero_zero_nat
!= ( suc @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(629,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(630,plain,
! [SV51: nat] :
( ( ! [SY162: nat] :
( ( ord_less_nat @ SV51 @ ( suc @ SY162 ) )
= ( ( SV51 = zero_zero_nat )
| ~ ! [SY163: nat] :
~ ~ ( ( SV51
!= ( suc @ SY163 ) )
| ~ ( ord_less_nat @ SY163 @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(631,plain,
! [SV52: nat > $o] :
( ( ! [SY164: nat] :
( ~ ( SV52 @ SY164 )
| ~ ! [SY165: nat] :
( ~ ( SV52 @ ( suc @ SY165 ) )
| ( SV52 @ SY165 ) )
| ( SV52 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(632,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= ( SV53 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(633,plain,
! [SV54: int] :
( ( ! [SY166: nat] :
( ( ( power_power_int @ SV54 @ SY166 )
= zero_zero_int )
= ( ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(634,plain,
! [SV55: nat] :
( ( ! [SY167: nat] :
( ( ( power_power_nat @ SV55 @ SY167 )
= zero_zero_nat )
= ( ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SY167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(635,plain,
! [SV56: nat] :
( ( ~ ( ( SV56 != zero_zero_nat ) )
| ~ ! [SY168: nat] :
( SV56
!= ( suc @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(636,plain,
! [SV57: nat] :
( ( ! [SY169: nat > $o] :
( ( ~ ! [SY170: nat] :
~ ~ ( ~ ( ord_less_nat @ SY170 @ ( suc @ SV57 ) )
| ~ ( SY169 @ SY170 ) ) )
= ( ( SY169 @ zero_zero_nat )
| ~ ! [SY171: nat] :
~ ~ ( ~ ( ord_less_nat @ SY171 @ SV57 )
| ~ ( SY169 @ ( suc @ SY171 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(637,plain,
! [SV58: nat] :
( ( ! [SY172: nat] :
( ~ ( ord_less_nat @ SV58 @ SY172 )
| ( SY172 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(638,plain,
! [SV59: nat] :
( ( ! [SY173: nat] :
( ( SV59
!= ( suc @ SY173 ) )
| ( SV59 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(639,plain,
! [SV60: nat] :
( ( ! [SY174: nat,SY175: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY174 )
| ~ ( ord_less_nat @ zero_zero_nat @ SY175 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SY175 ) @ ( power_power_nat @ SY174 @ SY175 ) )
= ( ord_less_eq_nat @ SV60 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(640,plain,
! [SV61: nat] :
( ( ~ ( ( SV61 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(641,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(642,plain,
! [SV63: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 )
| ( ( suc @ ( minus_minus_nat @ SV63 @ ( suc @ zero_zero_nat ) ) )
= SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(643,plain,
! [SV64: nat] :
( ( ! [SY176: nat] :
( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV64 )
| ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV64 @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(644,plain,
! [SV65: nat] :
( ( ! [SY177: nat > $o] :
( ( ! [SY178: nat] :
( ~ ( ord_less_nat @ SY178 @ ( suc @ SV65 ) )
| ( SY177 @ SY178 ) ) )
= ( ~ ( ~ ( SY177 @ zero_zero_nat )
| ~ ! [SY179: nat] :
( ~ ( ord_less_nat @ SY179 @ SV65 )
| ( SY177 @ ( suc @ SY179 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(645,plain,
! [SV66: nat] :
( ( zero_zero_nat
!= ( suc @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(646,plain,
! [SV67: polyno727731844poly_a] :
( ( ! [SY180: nat,SY181: nat] :
( ~ ( polyno1372495879olyh_a @ SV67 @ SY180 )
| ~ ( ord_less_nat @ SY181 @ SY180 )
| ( ( polyno1674775833reen_a @ SV67 @ SY181 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(647,plain,
! [SV68: nat > $o] :
( ( ! [SY182: nat] :
( ~ ( SV68 @ zero_zero_nat )
| ~ ! [SY183: nat] :
( ~ ( SV68 @ SY183 )
| ( SV68 @ ( suc @ SY183 ) ) )
| ( SV68 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(648,plain,
! [SV69: nat] :
( ( ! [SY184: nat,SY185: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV69 @ SY184 ) @ ( power_power_nat @ SY185 @ SY184 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY185 )
| ( ord_less_nat @ SV69 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(649,plain,
! [SV70: nat] :
( ( ! [SY186: nat] :
( ~ ( ord_less_nat @ SV70 @ SY186 )
| ( SY186 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(650,plain,
! [SV71: nat > $o] :
( ( ~ ~ ( SV71 @ zero_zero_nat )
| ~ ~ ! [SY187: nat] :
~ ( SV71 @ SY187 )
| ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(651,plain,
! [SV72: nat] :
( ( ! [SY189: nat] :
( ~ ( ( SV72 != zero_zero_nat ) )
| ( ( power_power_nat @ SV72 @ SY189 )
!= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(652,plain,
! [SV73: nat] :
( ( zero_zero_nat
!= ( suc @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(653,plain,
! [SV74: nat] :
( ( ~ ( ( SV74 != zero_zero_nat ) )
| ~ ! [SY190: nat] :
( SV74
!= ( suc @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(654,plain,
! [SV75: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= ( ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(655,plain,
! [SV76: nat > nat > $o] :
( ( ! [SY192: nat,SY193: nat] :
( ~ ! [SY194: nat] : ( SV76 @ SY194 @ zero_zero_nat )
| ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) )
| ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SY192 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(656,plain,
! [SV77: nat] :
( ( ~ ( ( SV77 != zero_zero_nat ) )
| ( ord_less_nat @ zero_zero_nat @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(657,plain,
! [SV78: nat] :
( ( ! [SY198: nat,SY199: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SY198 ) ) @ ( power_power_nat @ SY199 @ ( suc @ SY198 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY199 )
| ( ord_less_eq_nat @ SV78 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(658,plain,
! [SV79: nat] :
( ( ( suc @ SV79 )
!= zero_zero_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(659,plain,
! [SV80: polyno727731844poly_a] :
( ( ! [SY200: nat] :
( ~ ( polyno1372495879olyh_a @ SV80 @ ( suc @ SY200 ) )
| ( ( polyno578545843gree_a @ SV80 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(660,plain,
! [SV81: nat > $o] :
( ( ! [SY201: nat] :
( ~ ( SV81 @ zero_zero_nat )
| ~ ! [SY202: nat] :
( ~ ( SV81 @ SY202 )
| ( SV81 @ ( suc @ SY202 ) ) )
| ( SV81 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(661,plain,
! [SV1: nat] :
( ( ord_less_nat @ SV1 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(662,plain,
! [SV2: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[578]) ).
thf(663,plain,
! [SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= ( SV2 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[578]) ).
thf(664,plain,
! [SV3: nat] :
( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 = zero_zero_nat ) )
| ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[579]) ).
thf(665,plain,
! [SV3: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= ( SV3 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[579]) ).
thf(666,plain,
! [SV4: nat] :
( ( ord_less_nat @ SV4 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(667,plain,
! [SV5: nat] :
( ( ord_less_nat @ SV5 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(668,plain,
! [SV6: nat] :
( ( ord_less_nat @ SV6 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(669,plain,
! [SV7: nat] :
( ( ~ ( ( zero_zero_nat = SV7 )
| ( SV7 = zero_zero_nat ) )
| ~ ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[583]) ).
thf(670,plain,
! [SV7: nat] :
( ( ( zero_zero_nat = SV7 )
= ( SV7 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[583]) ).
thf(671,plain,
! [SV8: nat] :
( ( ord_less_nat @ SV8 @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(672,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno190918219poly_a @ SV82 )
= ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(673,plain,
! [SV10: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ( ord_less_nat @ zero_zero_nat @ SV10 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[588]) ).
thf(674,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[588]) ).
thf(675,plain,
! [SV11: nat] :
( ( ~ ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat = SV11 ) )
| ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[589]) ).
thf(676,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= ( zero_zero_nat = SV11 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[589]) ).
thf(677,plain,
! [SV12: nat] :
( ( ~ ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat = SV12 ) )
| ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[590]) ).
thf(678,plain,
! [SV12: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= ( zero_zero_nat = SV12 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[590]) ).
thf(679,plain,
! [SV13: nat] :
( ( ~ ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
| ( SV13 = zero_zero_nat ) )
| ~ ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[591]) ).
thf(680,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= ( SV13 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[591]) ).
thf(681,plain,
! [SV14: nat] :
( ( ~ ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
| ( SV14 = zero_zero_nat ) )
| ~ ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[592]) ).
thf(682,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= ( SV14 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[592]) ).
thf(683,plain,
! [SV15: nat] :
( ( ~ ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[593]) ).
thf(684,plain,
! [SV15: nat] :
( ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= ( SV15 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[593]) ).
thf(685,plain,
! [SV17: nat] :
( ( ord_less_nat @ ( semiri1382578993at_nat @ SV17 ) @ zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(686,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(687,plain,
! [SV19: nat] :
( ( ~ ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[597]) ).
thf(688,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= ( SV19 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[597]) ).
thf(689,plain,
! [SV20: nat] :
( ( ~ ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[598]) ).
thf(690,plain,
! [SV20: nat] :
( ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= ( SV20 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[598]) ).
thf(691,plain,
! [SV23: nat] :
( ( ~ ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[601]) ).
thf(692,plain,
! [SV23: nat] :
( ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= ( SV23 = zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[601]) ).
thf(693,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(694,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(695,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(696,plain,
! [SV87: nat,SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= ( ord_less_nat @ SV87 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(697,plain,
! [SV37: nat] :
( ( zero_zero_nat
= ( suc @ SV37 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(698,plain,
! [SV88: nat,SV38: nat] :
( ( ~ ( ord_less_eq_nat @ SV38 @ SV88 )
| ( ( minus_minus_nat @ SV38 @ SV88 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(699,plain,
! [SV89: nat,SV39: nat] :
( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV39 )
| ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV39 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(700,plain,
! [SV40: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV40 ) )
= $true )
| ( ( ~ ! [SY149: nat] :
( SV40
!= ( suc @ SY149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(701,plain,
! [SV90: nat,SV41: nat] :
( ( ! [SY203: nat] :
( ( ( power_power_nat @ SV41 @ SV90 )
!= ( power_power_nat @ SY203 @ SV90 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY203 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(702,plain,
! [SV91: nat,SV42: nat] :
( ( ! [SY204: nat] :
( ~ ( ord_less_eq_nat @ SV42 @ SV91 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV42 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SY204 ) @ ( power_power_nat @ SV91 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(703,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ~ ( SV43 @ zero_zero_nat )
| ~ ! [SY155: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY155 )
| ~ ~ ( SV43 @ SY155 )
| ~ ! [SY156: nat] :
~ ~ ( ~ ( ord_less_nat @ SY156 @ SY155 )
| ~ ~ ( SV43 @ SY156 ) ) )
| ( SV43 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(704,plain,
! [SV44: nat] :
( ( ( semiri1382578993at_nat @ ( suc @ SV44 ) )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(705,plain,
! [SV45: nat] :
( ( ( ~ ( ( SV45 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY157: nat] :
( SV45
!= ( suc @ SY157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(706,plain,
! [SV93: nat,SV46: nat] :
( ( ! [SY207: nat] :
( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
!= ( power_power_nat @ SY207 @ ( suc @ SV93 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY207 )
| ( SV46 = SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(707,plain,
! [SV94: nat,SV47: nat] :
( ( ! [SY208: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SV47 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY208 )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SY208 @ SV47 ) )
= ( SV94 = SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(708,plain,
! [SV48: nat] :
( ( ( suc @ SV48 )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(709,plain,
! [SV49: nat] :
( ( zero_zero_nat
= ( suc @ SV49 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(710,plain,
! [SV50: nat] :
( ( ~ ( ( SV50 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV50 ) )
| ~ ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[629]) ).
thf(711,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[629]) ).
thf(712,plain,
! [SV95: nat,SV51: nat] :
( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(713,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ~ ( SV52 @ SV96 )
| ~ ! [SY165: nat] :
( ~ ( SV52 @ ( suc @ SY165 ) )
| ( SV52 @ SY165 ) )
| ( SV52 @ zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(714,plain,
! [SV53: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[632]) ).
thf(715,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= ( SV53 != zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[632]) ).
thf(716,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= ( ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(717,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= ( ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(718,plain,
! [SV56: nat] :
( ( ( ~ ( ( SV56 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY168: nat] :
( SV56
!= ( suc @ SY168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(719,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(720,plain,
! [SV100: nat,SV58: nat] :
( ( ~ ( ord_less_nat @ SV58 @ SV100 )
| ( SV100 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(721,plain,
! [SV101: nat,SV59: nat] :
( ( ( SV59
!= ( suc @ SV101 ) )
| ( SV59 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(722,plain,
! [SV102: nat,SV60: nat] :
( ( ! [SY213: nat] :
( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
| ~ ( ord_less_nat @ zero_zero_nat @ SY213 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SY213 ) @ ( power_power_nat @ SV102 @ SY213 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(723,plain,
! [SV61: nat] :
( ( ( ~ ( ( SV61 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(724,plain,
! [SV62: nat] :
( ( ~ ( ( SV62 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV62 ) )
| ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[641]) ).
thf(725,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[641]) ).
thf(726,plain,
! [SV63: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV63 ) )
= $true )
| ( ( ( suc @ ( minus_minus_nat @ SV63 @ ( suc @ zero_zero_nat ) ) )
= SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(727,plain,
! [SV103: nat,SV64: nat] :
( ( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV64 )
| ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV64 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(728,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(729,plain,
! [SV66: nat] :
( ( zero_zero_nat
= ( suc @ SV66 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(730,plain,
! [SV105: nat,SV67: polyno727731844poly_a] :
( ( ! [SY216: nat] :
( ~ ( polyno1372495879olyh_a @ SV67 @ SV105 )
| ~ ( ord_less_nat @ SY216 @ SV105 )
| ( ( polyno1674775833reen_a @ SV67 @ SY216 )
= zero_zero_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(731,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ~ ( SV68 @ zero_zero_nat )
| ~ ! [SY183: nat] :
( ~ ( SV68 @ SY183 )
| ( SV68 @ ( suc @ SY183 ) ) )
| ( SV68 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(732,plain,
! [SV107: nat,SV69: nat] :
( ( ! [SY218: nat] :
( ~ ( ord_less_nat @ ( power_power_nat @ SV69 @ SV107 ) @ ( power_power_nat @ SY218 @ SV107 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY218 )
| ( ord_less_nat @ SV69 @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(733,plain,
! [SV108: nat,SV70: nat] :
( ( ~ ( ord_less_nat @ SV70 @ SV108 )
| ( SV108 != zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(734,plain,
! [SV71: nat > $o] :
( ( ( ~ ~ ( SV71 @ zero_zero_nat ) )
= $true )
| ( ( ~ ~ ! [SY187: nat] :
~ ( SV71 @ SY187 )
| ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(735,plain,
! [SV109: nat,SV72: nat] :
( ( ~ ( ( SV72 != zero_zero_nat ) )
| ( ( power_power_nat @ SV72 @ SV109 )
!= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(736,plain,
! [SV73: nat] :
( ( zero_zero_nat
= ( suc @ SV73 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(737,plain,
! [SV74: nat] :
( ( ( ~ ( ( SV74 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ! [SY190: nat] :
( SV74
!= ( suc @ SY190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(738,plain,
! [SV75: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[654]) ).
thf(739,plain,
! [SV75: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= ( ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[654]) ).
thf(740,plain,
! [SV110: nat,SV76: nat > nat > $o] :
( ( ! [SY219: nat] :
( ~ ! [SY194: nat] : ( SV76 @ SY194 @ zero_zero_nat )
| ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) )
| ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(741,plain,
! [SV77: nat] :
( ( ( ~ ( ( SV77 != zero_zero_nat ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(742,plain,
! [SV111: nat,SV78: nat] :
( ( ! [SY224: nat] :
( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SV111 ) ) @ ( power_power_nat @ SY224 @ ( suc @ SV111 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SY224 )
| ( ord_less_eq_nat @ SV78 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(743,plain,
! [SV79: nat] :
( ( ( suc @ SV79 )
= zero_zero_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(744,plain,
! [SV112: nat,SV80: polyno727731844poly_a] :
( ( ~ ( polyno1372495879olyh_a @ SV80 @ ( suc @ SV112 ) )
| ( ( polyno578545843gree_a @ SV80 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(745,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ~ ( SV81 @ zero_zero_nat )
| ~ ! [SY202: nat] :
( ~ ( SV81 @ SY202 )
| ( SV81 @ ( suc @ SY202 ) ) )
| ( SV81 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(746,plain,
! [SV2: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(747,plain,
! [SV3: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(748,plain,
! [SV7: nat] :
( ( ( ~ ( ( zero_zero_nat = SV7 )
| ( SV7 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(749,plain,
! [SV82: polyno727731844poly_a] :
( ( ~ ( ( polyno190918219poly_a @ SV82 )
| ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
| ~ ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[672]) ).
thf(750,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno190918219poly_a @ SV82 )
= ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[672]) ).
thf(751,plain,
! [SV10: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ( ord_less_nat @ zero_zero_nat @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(752,plain,
! [SV11: nat] :
( ( ( ~ ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat = SV11 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(753,plain,
! [SV12: nat] :
( ( ( ~ ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat = SV12 ) ) )
= $true )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(754,plain,
! [SV13: nat] :
( ( ( ~ ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
| ( SV13 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(755,plain,
! [SV14: nat] :
( ( ( ~ ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
| ( SV14 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(756,plain,
! [SV15: nat] :
( ( ( ~ ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(757,plain,
! [SV83: nat,SV18: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[686]) ).
thf(758,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[686]) ).
thf(759,plain,
! [SV19: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(760,plain,
! [SV20: nat] :
( ( ( ~ ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(761,plain,
! [SV23: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(762,plain,
! [SV84: nat,SV27: nat] :
( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
| ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) )
| ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[693]) ).
thf(763,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[693]) ).
thf(764,plain,
! [SV85: nat,SV29: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[694]) ).
thf(765,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[694]) ).
thf(766,plain,
! [SV86: nat,SV30: nat] :
( ( ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
| ( ord_less_eq_nat @ SV30 @ SV86 ) )
| ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[695]) ).
thf(767,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[695]) ).
thf(768,plain,
! [SV87: nat,SV35: nat] :
( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ( ord_less_nat @ SV87 @ SV35 ) )
| ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[696]) ).
thf(769,plain,
! [SV87: nat,SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= ( ord_less_nat @ SV87 @ SV35 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[696]) ).
thf(770,plain,
! [SV88: nat,SV38: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV38 @ SV88 ) )
= $true )
| ( ( ( minus_minus_nat @ SV38 @ SV88 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(771,plain,
! [SV89: nat,SV39: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV39 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV39 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(772,plain,
! [SV40: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV40 )
= $false )
| ( ( ~ ! [SY149: nat] :
( SV40
!= ( suc @ SY149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(773,plain,
! [SV114: nat,SV90: nat,SV41: nat] :
( ( ( ( power_power_nat @ SV41 @ SV90 )
!= ( power_power_nat @ SV114 @ SV90 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(774,plain,
! [SV115: nat,SV91: nat,SV42: nat] :
( ( ~ ( ord_less_eq_nat @ SV42 @ SV91 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV42 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SV115 ) @ ( power_power_nat @ SV91 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(775,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( ~ ( SV43 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY155: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY155 )
| ~ ~ ( SV43 @ SY155 )
| ~ ! [SY156: nat] :
~ ~ ( ~ ( ord_less_nat @ SY156 @ SY155 )
| ~ ~ ( SV43 @ SY156 ) ) )
| ( SV43 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(776,plain,
! [SV45: nat] :
( ( ( SV45 != zero_zero_nat )
= $false )
| ( ( ~ ! [SY157: nat] :
( SV45
!= ( suc @ SY157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(777,plain,
! [SV116: nat,SV93: nat,SV46: nat] :
( ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
!= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV116 )
| ( SV46 = SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(778,plain,
! [SV117: nat,SV94: nat,SV47: nat] :
( ( ~ ( ord_less_nat @ zero_zero_nat @ SV47 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(779,plain,
! [SV50: nat] :
( ( ( ~ ( ( SV50 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(780,plain,
! [SV95: nat,SV51: nat] :
( ( ~ ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
| ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[712]) ).
thf(781,plain,
! [SV95: nat,SV51: nat] :
( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[712]) ).
thf(782,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( ~ ( SV52 @ SV96 ) )
= $true )
| ( ( ~ ! [SY165: nat] :
( ~ ( SV52 @ ( suc @ SY165 ) )
| ( SV52 @ SY165 ) )
| ( SV52 @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(783,plain,
! [SV53: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(784,plain,
! [SV97: nat,SV54: int] :
( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
| ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
| ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[716]) ).
thf(785,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= ( ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[716]) ).
thf(786,plain,
! [SV98: nat,SV55: nat] :
( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
| ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
| ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[717]) ).
thf(787,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= ( ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[717]) ).
thf(788,plain,
! [SV56: nat] :
( ( ( SV56 != zero_zero_nat )
= $false )
| ( ( ~ ! [SY168: nat] :
( SV56
!= ( suc @ SY168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(789,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ~ ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
| ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[719]) ).
thf(790,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[719]) ).
thf(791,plain,
! [SV100: nat,SV58: nat] :
( ( ( ~ ( ord_less_nat @ SV58 @ SV100 ) )
= $true )
| ( ( SV100 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(792,plain,
! [SV101: nat,SV59: nat] :
( ( ( SV59
!= ( suc @ SV101 ) )
= $true )
| ( ( SV59 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(793,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV118 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(794,plain,
! [SV61: nat] :
( ( ( SV61 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(795,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(796,plain,
! [SV63: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV63 )
= $false )
| ( ( ( suc @ ( minus_minus_nat @ SV63 @ ( suc @ zero_zero_nat ) ) )
= SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(797,plain,
! [SV103: nat,SV64: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV64 ) )
= $true )
| ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV64 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(798,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ~ ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
| ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[728]) ).
thf(799,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[728]) ).
thf(800,plain,
! [SV119: nat,SV105: nat,SV67: polyno727731844poly_a] :
( ( ~ ( polyno1372495879olyh_a @ SV67 @ SV105 )
| ~ ( ord_less_nat @ SV119 @ SV105 )
| ( ( polyno1674775833reen_a @ SV67 @ SV119 )
= zero_zero_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(801,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( ~ ( SV68 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY183: nat] :
( ~ ( SV68 @ SY183 )
| ( SV68 @ ( suc @ SY183 ) ) )
| ( SV68 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(802,plain,
! [SV120: nat,SV107: nat,SV69: nat] :
( ( ~ ( ord_less_nat @ ( power_power_nat @ SV69 @ SV107 ) @ ( power_power_nat @ SV120 @ SV107 ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV120 )
| ( ord_less_nat @ SV69 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(803,plain,
! [SV108: nat,SV70: nat] :
( ( ( ~ ( ord_less_nat @ SV70 @ SV108 ) )
= $true )
| ( ( SV108 != zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(804,plain,
! [SV71: nat > $o] :
( ( ( ~ ( SV71 @ zero_zero_nat ) )
= $false )
| ( ( ~ ~ ! [SY187: nat] :
~ ( SV71 @ SY187 )
| ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(805,plain,
! [SV109: nat,SV72: nat] :
( ( ( ~ ( ( SV72 != zero_zero_nat ) ) )
= $true )
| ( ( ( power_power_nat @ SV72 @ SV109 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(806,plain,
! [SV74: nat] :
( ( ( SV74 != zero_zero_nat )
= $false )
| ( ( ~ ! [SY190: nat] :
( SV74
!= ( suc @ SY190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(807,plain,
! [SV75: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(808,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ~ ! [SY194: nat] : ( SV76 @ SY194 @ zero_zero_nat )
| ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) )
| ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(809,plain,
! [SV77: nat] :
( ( ( SV77 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(810,plain,
! [SV122: nat,SV111: nat,SV78: nat] :
( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SV111 ) ) @ ( power_power_nat @ SV122 @ ( suc @ SV111 ) ) )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV122 )
| ( ord_less_eq_nat @ SV78 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(811,plain,
! [SV112: nat,SV80: polyno727731844poly_a] :
( ( ( ~ ( polyno1372495879olyh_a @ SV80 @ ( suc @ SV112 ) ) )
= $true )
| ( ( ( polyno578545843gree_a @ SV80 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(812,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( ~ ( SV81 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY202: nat] :
( ~ ( SV81 @ SY202 )
| ( SV81 @ ( suc @ SY202 ) ) )
| ( SV81 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(813,plain,
! [SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(814,plain,
! [SV3: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(815,plain,
! [SV7: nat] :
( ( ( ( zero_zero_nat = SV7 )
| ( SV7 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(816,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( ( polyno190918219poly_a @ SV82 )
| ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(817,plain,
! [SV10: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(818,plain,
! [SV11: nat] :
( ( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat = SV11 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(819,plain,
! [SV12: nat] :
( ( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat = SV12 ) )
= $false )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(820,plain,
! [SV13: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
| ( SV13 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(821,plain,
! [SV14: nat] :
( ( ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
| ( SV14 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(822,plain,
! [SV15: nat] :
( ( ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(823,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(824,plain,
! [SV19: nat] :
( ( ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(825,plain,
! [SV20: nat] :
( ( ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(826,plain,
! [SV23: nat] :
( ( ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(827,plain,
! [SV84: nat,SV27: nat] :
( ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
| ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(828,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(829,plain,
! [SV86: nat,SV30: nat] :
( ( ( ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
| ( ord_less_eq_nat @ SV30 @ SV86 ) ) )
= $true )
| ( ( ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(830,plain,
! [SV87: nat,SV35: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ( ord_less_nat @ SV87 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(831,plain,
! [SV88: nat,SV38: nat] :
( ( ( ord_less_eq_nat @ SV38 @ SV88 )
= $false )
| ( ( ( minus_minus_nat @ SV38 @ SV88 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(832,plain,
! [SV89: nat,SV39: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV39 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ SV39 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(833,plain,
! [SV40: nat] :
( ( ( ! [SY149: nat] :
( SV40
!= ( suc @ SY149 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(834,plain,
! [SV114: nat,SV90: nat,SV41: nat] :
( ( ( ( power_power_nat @ SV41 @ SV90 )
!= ( power_power_nat @ SV114 @ SV90 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(835,plain,
! [SV115: nat,SV91: nat,SV42: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV42 @ SV91 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV42 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SV115 ) @ ( power_power_nat @ SV91 @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(836,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( SV43 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY155: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY155 )
| ~ ~ ( SV43 @ SY155 )
| ~ ! [SY156: nat] :
~ ~ ( ~ ( ord_less_nat @ SY156 @ SY155 )
| ~ ~ ( SV43 @ SY156 ) ) )
| ( SV43 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(837,plain,
! [SV45: nat] :
( ( ( SV45 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY157: nat] :
( SV45
!= ( suc @ SY157 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(838,plain,
! [SV116: nat,SV93: nat,SV46: nat] :
( ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
!= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV116 )
| ( SV46 = SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(839,plain,
! [SV117: nat,SV94: nat,SV47: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV47 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(840,plain,
! [SV50: nat] :
( ( ( ( SV50 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( ~ ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(841,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(842,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( SV52 @ SV96 )
= $false )
| ( ( ~ ! [SY165: nat] :
( ~ ( SV52 @ ( suc @ SY165 ) )
| ( SV52 @ SY165 ) )
| ( SV52 @ zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(843,plain,
! [SV53: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
| ( SV53 != zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(844,plain,
! [SV97: nat,SV54: int] :
( ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
| ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(845,plain,
! [SV98: nat,SV55: nat] :
( ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
| ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(846,plain,
! [SV56: nat] :
( ( ( SV56 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY168: nat] :
( SV56
!= ( suc @ SY168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(847,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(848,plain,
! [SV100: nat,SV58: nat] :
( ( ( ord_less_nat @ SV58 @ SV100 )
= $false )
| ( ( SV100 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(849,plain,
! [SV101: nat,SV59: nat] :
( ( ( SV59
= ( suc @ SV101 ) )
= $false )
| ( ( SV59 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(850,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV60 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV118 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(851,plain,
! [SV61: nat] :
( ( ( SV61 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV61 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(852,plain,
! [SV62: nat] :
( ( ( ( SV62 != zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(853,plain,
! [SV103: nat,SV64: nat] :
( ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ SV64 )
= $false )
| ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ SV64 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(854,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(855,plain,
! [SV119: nat,SV105: nat,SV67: polyno727731844poly_a] :
( ( ( ~ ( polyno1372495879olyh_a @ SV67 @ SV105 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV119 @ SV105 )
| ( ( polyno1674775833reen_a @ SV67 @ SV119 )
= zero_zero_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(856,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( SV68 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY183: nat] :
( ~ ( SV68 @ SY183 )
| ( SV68 @ ( suc @ SY183 ) ) )
| ( SV68 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(857,plain,
! [SV120: nat,SV107: nat,SV69: nat] :
( ( ( ~ ( ord_less_nat @ ( power_power_nat @ SV69 @ SV107 ) @ ( power_power_nat @ SV120 @ SV107 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV120 )
| ( ord_less_nat @ SV69 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(858,plain,
! [SV108: nat,SV70: nat] :
( ( ( ord_less_nat @ SV70 @ SV108 )
= $false )
| ( ( SV108 != zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(859,plain,
! [SV71: nat > $o] :
( ( ( SV71 @ zero_zero_nat )
= $true )
| ( ( ~ ~ ! [SY187: nat] :
~ ( SV71 @ SY187 )
| ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(860,plain,
! [SV109: nat,SV72: nat] :
( ( ( SV72 != zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV72 @ SV109 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(861,plain,
! [SV74: nat] :
( ( ( SV74 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY190: nat] :
( SV74
!= ( suc @ SY190 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(862,plain,
! [SV75: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(863,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ( ~ ! [SY194: nat] : ( SV76 @ SY194 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) )
| ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(864,plain,
! [SV77: nat] :
( ( ( SV77 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(865,plain,
! [SV122: nat,SV111: nat,SV78: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SV111 ) ) @ ( power_power_nat @ SV122 @ ( suc @ SV111 ) ) ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV122 )
| ( ord_less_eq_nat @ SV78 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(866,plain,
! [SV112: nat,SV80: polyno727731844poly_a] :
( ( ( polyno1372495879olyh_a @ SV80 @ ( suc @ SV112 ) )
= $false )
| ( ( ( polyno578545843gree_a @ SV80 )
= zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(867,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( SV81 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY202: nat] :
( ~ ( SV81 @ SY202 )
| ( SV81 @ ( suc @ SY202 ) ) )
| ( SV81 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(868,plain,
! [SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(869,plain,
! [SV2: nat] :
( ( ( SV2 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(870,plain,
! [SV3: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(871,plain,
! [SV3: nat] :
( ( ( SV3 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(872,plain,
! [SV7: nat] :
( ( ( zero_zero_nat = SV7 )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(873,plain,
! [SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $false )
| ( ( ~ ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(874,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ( polyno190918219poly_a @ SV82 )
| ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(875,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(876,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(877,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(878,plain,
! [SV11: nat] :
( ( ( zero_zero_nat = SV11 )
= $false )
| ( ( ~ ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(879,plain,
! [SV12: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $false )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(880,plain,
! [SV12: nat] :
( ( ( zero_zero_nat = SV12 )
= $false )
| ( ( ~ ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(881,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(882,plain,
! [SV13: nat] :
( ( ( SV13 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(883,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $false )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[821]) ).
thf(884,plain,
! [SV14: nat] :
( ( ( SV14 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[821]) ).
thf(885,plain,
! [SV15: nat] :
( ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(886,plain,
! [SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(887,plain,
! [SV83: nat,SV18: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(888,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(889,plain,
! [SV19: nat] :
( ( ( SV19 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(890,plain,
! [SV20: nat] :
( ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(891,plain,
! [SV20: nat] :
( ( ( SV20 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(892,plain,
! [SV23: nat] :
( ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[826]) ).
thf(893,plain,
! [SV23: nat] :
( ( ( SV23 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[826]) ).
thf(894,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
| ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(895,plain,
! [SV85: nat,SV29: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(896,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
| ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(897,plain,
! [SV87: nat,SV35: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ( ord_less_nat @ SV87 @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(898,plain,
! [SV40: nat] :
( ( ( SV40
!= ( suc @ ( sK1_SY149 @ SV40 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV40 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[833]) ).
thf(899,plain,
! [SV114: nat,SV90: nat,SV41: nat] :
( ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(900,plain,
! [SV115: nat,SV91: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ SV42 @ SV91 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV42 )
| ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SV115 ) @ ( power_power_nat @ SV91 @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(901,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( ~ ! [SY155: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY155 )
| ~ ~ ( SV43 @ SY155 )
| ~ ! [SY156: nat] :
~ ~ ( ~ ( ord_less_nat @ SY156 @ SY155 )
| ~ ~ ( SV43 @ SY156 ) ) ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(902,plain,
! [SV45: nat] :
( ( ( ! [SY157: nat] :
( SV45
!= ( suc @ SY157 ) ) )
= $false )
| ( ( SV45 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(903,plain,
! [SV116: nat,SV93: nat,SV46: nat] :
( ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV116 )
| ( SV46 = SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(904,plain,
! [SV117: nat,SV94: nat,SV47: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
| ~ ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(905,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(906,plain,
! [SV50: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false )
| ( ( ~ ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(907,plain,
! [SV95: nat,SV51: nat] :
( ( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(908,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( ~ ! [SY165: nat] :
( ~ ( SV52 @ ( suc @ SY165 ) )
| ( SV52 @ SY165 ) ) )
= $true )
| ( ( SV52 @ zero_zero_nat )
= $true )
| ( ( SV52 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(909,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(910,plain,
! [SV53: nat] :
( ( ( SV53 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(911,plain,
! [SV97: nat,SV54: int] :
( ( ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
| ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(912,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
| ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(913,plain,
! [SV56: nat] :
( ( ( ! [SY168: nat] :
( SV56
!= ( suc @ SY168 ) ) )
= $false )
| ( ( SV56 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(914,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(915,plain,
! [SV58: nat,SV100: nat] :
( ( ( SV100 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV58 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(916,plain,
! [SV101: nat,SV59: nat] :
( ( ( SV59 = zero_zero_nat )
= $false )
| ( ( SV59
= ( suc @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(917,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV118 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(918,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(919,plain,
! [SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(920,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(921,plain,
! [SV119: nat,SV105: nat,SV67: polyno727731844poly_a] :
( ( ( polyno1372495879olyh_a @ SV67 @ SV105 )
= $false )
| ( ( ~ ( ord_less_nat @ SV119 @ SV105 )
| ( ( polyno1674775833reen_a @ SV67 @ SV119 )
= zero_zero_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(922,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( ~ ! [SY183: nat] :
( ~ ( SV68 @ SY183 )
| ( SV68 @ ( suc @ SY183 ) ) ) )
= $true )
| ( ( SV68 @ SV106 )
= $true )
| ( ( SV68 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(923,plain,
! [SV120: nat,SV107: nat,SV69: nat] :
( ( ( ord_less_nat @ ( power_power_nat @ SV69 @ SV107 ) @ ( power_power_nat @ SV120 @ SV107 ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV120 )
| ( ord_less_nat @ SV69 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(924,plain,
! [SV70: nat,SV108: nat] :
( ( ( SV108 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV70 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(925,plain,
! [SV71: nat > $o] :
( ( ( ~ ~ ! [SY187: nat] :
~ ( SV71 @ SY187 ) )
= $true )
| ( ( ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(926,plain,
! [SV109: nat,SV72: nat] :
( ( ( SV72 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV72 @ SV109 )
!= zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(927,plain,
! [SV74: nat] :
( ( ( ! [SY190: nat] :
( SV74
!= ( suc @ SY190 ) ) )
= $false )
| ( ( SV74 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(928,plain,
! [SV75: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(929,plain,
! [SV75: nat] :
( ( ( ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(930,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ( ! [SY194: nat] : ( SV76 @ SY194 @ zero_zero_nat ) )
= $false )
| ( ( ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) )
| ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(931,plain,
! [SV122: nat,SV111: nat,SV78: nat] :
( ( ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SV111 ) ) @ ( power_power_nat @ SV122 @ ( suc @ SV111 ) ) )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV122 )
| ( ord_less_eq_nat @ SV78 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(932,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( ~ ! [SY202: nat] :
( ~ ( SV81 @ SY202 )
| ( SV81 @ ( suc @ SY202 ) ) ) )
= $true )
| ( ( SV81 @ SV113 )
= $true )
| ( ( SV81 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(933,plain,
! [SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(934,plain,
! [SV2: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) )
= $false )
| ( ( SV2 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(935,plain,
! [SV3: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true )
| ( ( ~ ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(936,plain,
! [SV3: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) )
= $false )
| ( ( SV3 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(937,plain,
! [SV7: nat] :
( ( ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) )
= $false )
| ( ( zero_zero_nat = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(938,plain,
! [SV7: nat] :
( ( ( ( zero_zero_nat != SV7 )
| ( SV7 != zero_zero_nat ) )
= $false )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(939,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno190918219poly_a @ SV82 )
= $false )
| ( ( ~ ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(940,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(941,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(942,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(943,plain,
! [SV11: nat] :
( ( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(944,plain,
! [SV11: nat] :
( ( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
| ( zero_zero_nat != SV11 ) )
= $false )
| ( ( zero_zero_nat = SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(945,plain,
! [SV12: nat] :
( ( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) )
= $false )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(946,plain,
! [SV12: nat] :
( ( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
| ( zero_zero_nat != SV12 ) )
= $false )
| ( ( zero_zero_nat = SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(947,plain,
! [SV13: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) )
= $false )
| ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(948,plain,
! [SV13: nat] :
( ( ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
| ( SV13 != zero_zero_nat ) )
= $false )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(949,plain,
! [SV14: nat] :
( ( ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) )
= $false )
| ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(950,plain,
! [SV14: nat] :
( ( ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
| ( SV14 != zero_zero_nat ) )
= $false )
| ( ( SV14 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(951,plain,
! [SV15: nat] :
( ( ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(952,plain,
! [SV15: nat] :
( ( ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
| ( SV15 != zero_zero_nat ) )
= $false )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(953,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(954,plain,
! [SV83: nat,SV18: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(955,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(956,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
| ( SV19 != zero_zero_nat ) )
= $false )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(957,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(958,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
| ( SV20 != zero_zero_nat ) )
= $false )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(959,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(960,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
| ( SV23 != zero_zero_nat ) )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(961,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(962,plain,
! [SV27: nat,SV84: nat] :
( ( ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(963,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(964,plain,
! [SV85: nat,SV29: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(965,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(966,plain,
! [SV86: nat,SV30: nat] :
( ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $false )
| ( ( ~ ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(967,plain,
! [SV87: nat,SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(968,plain,
! [SV35: nat,SV87: nat] :
( ( ( ord_less_nat @ SV87 @ SV35 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(969,plain,
! [SV40: nat] :
( ( ( SV40
= ( suc @ ( sK1_SY149 @ SV40 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(970,plain,
! [SV90: nat,SV114: nat,SV41: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV41 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true )
| ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(971,plain,
! [SV91: nat,SV115: nat,SV42: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV42 ) )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SV115 ) @ ( power_power_nat @ SV91 @ SV115 ) )
= $true )
| ( ( ord_less_eq_nat @ SV42 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(972,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( ! [SY155: nat] :
( ~ ( ord_less_nat @ zero_zero_nat @ SY155 )
| ~ ~ ( SV43 @ SY155 )
| ~ ! [SY156: nat] :
~ ~ ( ~ ( ord_less_nat @ SY156 @ SY155 )
| ~ ~ ( SV43 @ SY156 ) ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(973,plain,
! [SV45: nat] :
( ( ( SV45
!= ( suc @ ( sK2_SY157 @ SV45 ) ) )
= $false )
| ( ( SV45 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[902]) ).
thf(974,plain,
! [SV93: nat,SV116: nat,SV46: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV46 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV116 )
| ( SV46 = SV116 ) )
= $true )
| ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(975,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV94 ) )
= $true )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(976,plain,
! [SV50: nat] :
( ( ( SV50 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(977,plain,
! [SV50: nat] :
( ( ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(978,plain,
! [SV95: nat,SV51: nat] :
( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(979,plain,
! [SV95: nat,SV51: nat] :
( ( ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(980,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( ! [SY165: nat] :
( ~ ( SV52 @ ( suc @ SY165 ) )
| ( SV52 @ SY165 ) ) )
= $false )
| ( ( SV52 @ zero_zero_nat )
= $true )
| ( ( SV52 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(981,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(982,plain,
! [SV53: nat] :
( ( ( SV53 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(983,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(984,plain,
! [SV97: nat,SV54: int] :
( ( ( ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(985,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(986,plain,
! [SV98: nat,SV55: nat] :
( ( ( ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(987,plain,
! [SV56: nat] :
( ( ( SV56
!= ( suc @ ( sK3_SY168 @ SV56 ) ) )
= $false )
| ( ( SV56 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[913]) ).
thf(988,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(989,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(990,plain,
! [SV60: nat,SV118: nat,SV102: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV102 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV118 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(991,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $true )
| ( ( ~ ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(992,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(993,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(994,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(995,plain,
! [SV67: polyno727731844poly_a,SV105: nat,SV119: nat] :
( ( ( ~ ( ord_less_nat @ SV119 @ SV105 ) )
= $true )
| ( ( ( polyno1674775833reen_a @ SV67 @ SV119 )
= zero_zero_nat )
= $true )
| ( ( polyno1372495879olyh_a @ SV67 @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(996,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( ! [SY183: nat] :
( ~ ( SV68 @ SY183 )
| ( SV68 @ ( suc @ SY183 ) ) ) )
= $false )
| ( ( SV68 @ SV106 )
= $true )
| ( ( SV68 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(997,plain,
! [SV107: nat,SV69: nat,SV120: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV120 ) )
= $true )
| ( ( ord_less_nat @ SV69 @ SV120 )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV69 @ SV107 ) @ ( power_power_nat @ SV120 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(998,plain,
! [SV71: nat > $o] :
( ( ( ~ ! [SY187: nat] :
~ ( SV71 @ SY187 ) )
= $false )
| ( ( ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(999,plain,
! [SV109: nat,SV72: nat] :
( ( ( ( power_power_nat @ SV72 @ SV109 )
= zero_zero_nat )
= $false )
| ( ( SV72 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1000,plain,
! [SV74: nat] :
( ( ( SV74
!= ( suc @ ( sK4_SY190 @ SV74 ) ) )
= $false )
| ( ( SV74 = zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[927]) ).
thf(1001,plain,
! [SV75: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1002,plain,
! [SV75: nat] :
( ( ( ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(1003,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) )
| ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[930]) ).
thf(1004,plain,
! [SV111: nat,SV78: nat,SV122: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV122 ) )
= $true )
| ( ( ord_less_eq_nat @ SV78 @ SV122 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SV111 ) ) @ ( power_power_nat @ SV122 @ ( suc @ SV111 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1005,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( ! [SY202: nat] :
( ~ ( SV81 @ SY202 )
| ( SV81 @ ( suc @ SY202 ) ) ) )
= $false )
| ( ( SV81 @ SV113 )
= $true )
| ( ( SV81 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1006,plain,
! [SV2: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 )
| ( SV2 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1007,plain,
! [SV2: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= $false )
| ( ( SV2 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(1008,plain,
! [SV2: nat] :
( ( ( SV2 != zero_zero_nat )
= $false )
| ( ( SV2 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(1009,plain,
! [SV3: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 )
| ( SV3 != zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1010,plain,
! [SV3: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= $false )
| ( ( SV3 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1011,plain,
! [SV3: nat] :
( ( ( SV3 != zero_zero_nat )
= $false )
| ( ( SV3 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[936]) ).
thf(1012,plain,
! [SV7: nat] :
( ( ( zero_zero_nat != SV7 )
= $false )
| ( ( zero_zero_nat = SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1013,plain,
! [SV7: nat] :
( ( ( SV7 != zero_zero_nat )
= $false )
| ( ( zero_zero_nat = SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(1014,plain,
! [SV7: nat] :
( ( ( zero_zero_nat != SV7 )
= $false )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1015,plain,
! [SV7: nat] :
( ( ( SV7 != zero_zero_nat )
= $false )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1016,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $false )
| ( ( polyno190918219poly_a @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1017,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( polyno190918219poly_a @ SV82 )
| ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $false )
| ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1018,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1019,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1020,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1021,plain,
! [SV10: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV10 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1022,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(1023,plain,
! [SV11: nat] :
( ( ( zero_zero_nat != SV11 )
= $false )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(1024,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
!= ( semiri1382578993at_nat @ SV11 ) )
= $false )
| ( ( zero_zero_nat = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1025,plain,
! [SV11: nat] :
( ( ( zero_zero_nat != SV11 )
= $false )
| ( ( zero_zero_nat = SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1026,plain,
! [SV12: nat] :
( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
= $false )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1027,plain,
! [SV12: nat] :
( ( ( zero_zero_nat != SV12 )
= $false )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1028,plain,
! [SV12: nat] :
( ( ( zero_zero_int
!= ( semiri2019852685at_int @ SV12 ) )
= $false )
| ( ( zero_zero_nat = SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1029,plain,
! [SV12: nat] :
( ( ( zero_zero_nat != SV12 )
= $false )
| ( ( zero_zero_nat = SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1030,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
= $false )
| ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1031,plain,
! [SV13: nat] :
( ( ( SV13 != zero_zero_nat )
= $false )
| ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1032,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
!= zero_zero_nat )
= $false )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1033,plain,
! [SV13: nat] :
( ( ( SV13 != zero_zero_nat )
= $false )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1034,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
= $false )
| ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1035,plain,
! [SV14: nat] :
( ( ( SV14 != zero_zero_nat )
= $false )
| ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1036,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
!= zero_zero_int )
= $false )
| ( ( SV14 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1037,plain,
! [SV14: nat] :
( ( ( SV14 != zero_zero_nat )
= $false )
| ( ( SV14 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1038,plain,
! [SV15: nat] :
( ( ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1039,plain,
! [SV15: nat] :
( ( ( SV15 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1040,plain,
! [SV15: nat] :
( ( ( ~ ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) ) )
= $false )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1041,plain,
! [SV15: nat] :
( ( ( SV15 != zero_zero_nat )
= $false )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1042,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1043,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1044,plain,
! [SV18: nat,SV83: nat] :
( ( ( SV83 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1045,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(1046,plain,
! [SV19: nat] :
( ( ( SV19 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[955]) ).
thf(1047,plain,
! [SV19: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat ) )
= $false )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1048,plain,
! [SV19: nat] :
( ( ( SV19 != zero_zero_nat )
= $false )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(1049,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int ) )
= $false )
| ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1050,plain,
! [SV20: nat] :
( ( ( SV20 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1051,plain,
! [SV20: nat] :
( ( ( ~ ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int ) )
= $false )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1052,plain,
! [SV20: nat] :
( ( ( SV20 != zero_zero_nat )
= $false )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1053,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1054,plain,
! [SV23: nat] :
( ( ( SV23 != zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1055,plain,
! [SV23: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV23 @ zero_zero_nat ) )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(1056,plain,
! [SV23: nat] :
( ( ( SV23 != zero_zero_nat )
= $false )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(1057,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1058,plain,
! [SV27: nat,SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1059,plain,
! [SV84: nat,SV27: nat] :
( ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1060,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1061,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1062,plain,
! [SV29: nat,SV85: nat] :
( ( ( SV85 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1063,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $false )
| ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1064,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
| ~ ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $false )
| ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1065,plain,
! [SV87: nat,SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1066,plain,
! [SV87: nat,SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
| ~ ( ord_less_nat @ SV87 @ SV35 ) )
= $false )
| ( ( ord_less_nat @ SV87 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1067,plain,
! [SV90: nat,SV114: nat,SV41: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
| ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true )
| ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1068,plain,
! [SV91: nat,SV115: nat,SV42: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV42 )
= $false )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV42 @ SV115 ) @ ( power_power_nat @ SV91 @ SV115 ) )
= $true )
| ( ( ord_less_eq_nat @ SV42 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1069,plain,
! [SV43: nat > $o,SV92: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ! [SY230: nat] :
~ ~ ( ~ ( ord_less_nat @ SY230 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SY230 ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[972]) ).
thf(1070,plain,
! [SV45: nat] :
( ( ( SV45
= ( suc @ ( sK2_SY157 @ SV45 ) ) )
= $true )
| ( ( SV45 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1071,plain,
! [SV93: nat,SV116: nat,SV46: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV116 )
| ( SV46 = SV116 ) )
= $true )
| ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1072,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1073,plain,
! [SV50: nat] :
( ( ( ~ ( ( SV50 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( SV50 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1074,plain,
! [SV50: nat] :
( ( ( ~ ( ( SV50 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1075,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1076,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1077,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1078,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1079,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( ~ ( SV52 @ ( suc @ ( sK7_SY165 @ SV96 @ SV52 ) ) )
| ( SV52 @ ( sK7_SY165 @ SV96 @ SV52 ) ) )
= $false )
| ( ( SV52 @ zero_zero_nat )
= $true )
| ( ( SV52 @ SV96 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[980]) ).
thf(1080,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1081,plain,
! [SV53: nat] :
( ( ( ~ ( ( SV53 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1082,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 )
| ~ ( ( SV53 != zero_zero_nat ) ) )
= $false )
| ( ( SV53 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1083,plain,
! [SV97: nat,SV54: int] :
( ( ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1084,plain,
! [SV97: nat,SV54: int] :
( ( ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $true )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1085,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $false )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1086,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1087,plain,
! [SV56: nat] :
( ( ( SV56
= ( suc @ ( sK3_SY168 @ SV56 ) ) )
= $true )
| ( ( SV56 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1088,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1089,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( SV99 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1090,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1091,plain,
! [SV60: nat,SV118: nat,SV102: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV118 )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1092,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) )
| ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1093,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1094,plain,
! [SV62: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1095,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
| ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[993]) ).
thf(1096,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1097,plain,
! [SV67: polyno727731844poly_a,SV105: nat,SV119: nat] :
( ( ( ord_less_nat @ SV119 @ SV105 )
= $false )
| ( ( ( polyno1674775833reen_a @ SV67 @ SV119 )
= zero_zero_nat )
= $true )
| ( ( polyno1372495879olyh_a @ SV67 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1098,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( ~ ( SV68 @ ( sK9_SY183 @ SV106 @ SV68 ) )
| ( SV68 @ ( suc @ ( sK9_SY183 @ SV106 @ SV68 ) ) ) )
= $false )
| ( ( SV68 @ SV106 )
= $true )
| ( ( SV68 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[996]) ).
thf(1099,plain,
! [SV107: nat,SV69: nat,SV120: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV120 )
= $false )
| ( ( ord_less_nat @ SV69 @ SV120 )
= $true )
| ( ( ord_less_nat @ ( power_power_nat @ SV69 @ SV107 ) @ ( power_power_nat @ SV120 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1100,plain,
! [SV71: nat > $o] :
( ( ( ! [SY187: nat] :
~ ( SV71 @ SY187 ) )
= $true )
| ( ( ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1101,plain,
! [SV74: nat] :
( ( ( SV74
= ( suc @ ( sK4_SY190 @ SV74 ) ) )
= $true )
| ( ( SV74 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1102,plain,
! [SV75: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1103,plain,
! [SV75: nat] :
( ( ( ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1104,plain,
! [SV123: nat,SV75: nat] :
( ( ( SV75
!= ( suc @ SV123 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1105,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ( ~ ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) ) )
= $true )
| ( ( ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1106,plain,
! [SV111: nat,SV78: nat,SV122: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV122 )
= $false )
| ( ( ord_less_eq_nat @ SV78 @ SV122 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV78 @ ( suc @ SV111 ) ) @ ( power_power_nat @ SV122 @ ( suc @ SV111 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1107,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( ~ ( SV81 @ ( sK10_SY202 @ SV113 @ SV81 ) )
| ( SV81 @ ( suc @ ( sK10_SY202 @ SV113 @ SV81 ) ) ) )
= $false )
| ( ( SV81 @ SV113 )
= $true )
| ( ( SV81 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1005]) ).
thf(1108,plain,
! [SV2: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1109,plain,
! [SV2: nat] :
( ( ( SV2 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1110,plain,
! [SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= $true )
| ( ( SV2 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1111,plain,
! [SV2: nat] :
( ( ( SV2 = zero_zero_nat )
= $true )
| ( ( SV2 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1112,plain,
! [SV3: nat] :
( ( ( ~ ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1009]) ).
thf(1113,plain,
! [SV3: nat] :
( ( ( SV3 != zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1009]) ).
thf(1114,plain,
! [SV3: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= $true )
| ( ( SV3 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1115,plain,
! [SV3: nat] :
( ( ( SV3 = zero_zero_nat )
= $true )
| ( ( SV3 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1116,plain,
! [SV7: nat] :
( ( ( zero_zero_nat = SV7 )
= $true )
| ( ( zero_zero_nat = SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1117,plain,
! [SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $true )
| ( ( zero_zero_nat = SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1118,plain,
! [SV7: nat] :
( ( ( zero_zero_nat = SV7 )
= $true )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1119,plain,
! [SV7: nat] :
( ( ( SV7 = zero_zero_nat )
= $true )
| ( ( SV7 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1120,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( polyno190918219poly_a @ SV82 ) )
= $false )
| ( ( polyno190918219poly_a @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1121,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $false )
| ( ( polyno190918219poly_a @ SV82 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1122,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( polyno190918219poly_a @ SV82 ) )
= $false )
| ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1123,plain,
! [SV82: polyno727731844poly_a] :
( ( ( ~ ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat ) )
= $false )
| ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1124,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1125,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1126,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ SV10 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1127,plain,
! [SV10: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1128,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $true )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1129,plain,
! [SV11: nat] :
( ( ( zero_zero_nat = SV11 )
= $true )
| ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1130,plain,
! [SV11: nat] :
( ( ( zero_zero_nat
= ( semiri1382578993at_nat @ SV11 ) )
= $true )
| ( ( zero_zero_nat = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1131,plain,
! [SV11: nat] :
( ( ( zero_zero_nat = SV11 )
= $true )
| ( ( zero_zero_nat = SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1132,plain,
! [SV12: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $true )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1133,plain,
! [SV12: nat] :
( ( ( zero_zero_nat = SV12 )
= $true )
| ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1134,plain,
! [SV12: nat] :
( ( ( zero_zero_int
= ( semiri2019852685at_int @ SV12 ) )
= $true )
| ( ( zero_zero_nat = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1135,plain,
! [SV12: nat] :
( ( ( zero_zero_nat = SV12 )
= $true )
| ( ( zero_zero_nat = SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1136,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $true )
| ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1137,plain,
! [SV13: nat] :
( ( ( SV13 = zero_zero_nat )
= $true )
| ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1138,plain,
! [SV13: nat] :
( ( ( ( semiri1382578993at_nat @ SV13 )
= zero_zero_nat )
= $true )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1139,plain,
! [SV13: nat] :
( ( ( SV13 = zero_zero_nat )
= $true )
| ( ( SV13 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1140,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $true )
| ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1141,plain,
! [SV14: nat] :
( ( ( SV14 = zero_zero_nat )
= $true )
| ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1142,plain,
! [SV14: nat] :
( ( ( ( semiri2019852685at_int @ SV14 )
= zero_zero_int )
= $true )
| ( ( SV14 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1143,plain,
! [SV14: nat] :
( ( ( SV14 = zero_zero_nat )
= $true )
| ( ( SV14 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1144,plain,
! [SV15: nat] :
( ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1145,plain,
! [SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1146,plain,
! [SV15: nat] :
( ( ( ord_less_nat @ SV15 @ ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1147,plain,
! [SV15: nat] :
( ( ( SV15 = zero_zero_nat )
= $true )
| ( ( SV15 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1148,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1149,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1150,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1151,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $false )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1152,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1153,plain,
! [SV19: nat] :
( ( ( SV19 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1154,plain,
! [SV19: nat] :
( ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ SV19 ) @ zero_zero_nat )
= $true )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1155,plain,
! [SV19: nat] :
( ( ( SV19 = zero_zero_nat )
= $true )
| ( ( SV19 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1156,plain,
! [SV20: nat] :
( ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $true )
| ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1157,plain,
! [SV20: nat] :
( ( ( SV20 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1050]) ).
thf(1158,plain,
! [SV20: nat] :
( ( ( ord_less_eq_int @ ( semiri2019852685at_int @ SV20 ) @ zero_zero_int )
= $true )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1159,plain,
! [SV20: nat] :
( ( ( SV20 = zero_zero_nat )
= $true )
| ( ( SV20 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1160,plain,
! [SV23: nat] :
( ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1161,plain,
! [SV23: nat] :
( ( ( SV23 = zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1162,plain,
! [SV23: nat] :
( ( ( ord_less_eq_nat @ SV23 @ zero_zero_nat )
= $true )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1163,plain,
! [SV23: nat] :
( ( ( SV23 = zero_zero_nat )
= $true )
| ( ( SV23 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1164,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
= $false )
| ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1165,plain,
! [SV27: nat,SV84: nat] :
( ( ( ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1166,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1167,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
| ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1168,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1169,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1170,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1171,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
| ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $false )
| ( ( SV85 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1172,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
= $false )
| ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1173,plain,
! [SV86: nat,SV30: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $false )
| ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1174,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
!= zero_zero_nat )
= $false )
| ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1175,plain,
! [SV86: nat,SV30: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV30 @ SV86 ) )
= $false )
| ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1176,plain,
! [SV87: nat,SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1177,plain,
! [SV35: nat,SV87: nat] :
( ( ( ~ ( ord_less_nat @ SV87 @ SV35 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1178,plain,
! [SV87: nat,SV35: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) ) )
= $false )
| ( ( ord_less_nat @ SV87 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1179,plain,
! [SV35: nat,SV87: nat] :
( ( ( ~ ( ord_less_nat @ SV87 @ SV35 ) )
= $false )
| ( ( ord_less_nat @ SV87 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1180,plain,
! [SV41: nat,SV90: nat,SV114: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV114 ) )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
= $false )
| ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1181,plain,
! [SV43: nat > $o,SV92: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( sK6_SY155 @ SV92 @ SV43 ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1182,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( ~ ~ ( SV43 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ! [SY230: nat] :
~ ~ ( ~ ( ord_less_nat @ SY230 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SY230 ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1183,plain,
! [SV93: nat,SV46: nat,SV116: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV116 ) )
= $true )
| ( ( SV46 = SV116 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
= $false )
| ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1184,plain,
! [SV47: nat,SV94: nat,SV117: nat] :
( ( ( ~ ( ord_less_eq_nat @ zero_zero_nat @ SV117 ) )
= $true )
| ( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1185,plain,
! [SV50: nat] :
( ( ( ~ ( ( SV50 != zero_zero_nat ) ) )
= $false )
| ( ( SV50 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1186,plain,
! [SV50: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV50 ) )
= $false )
| ( ( SV50 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1187,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1188,plain,
! [SV50: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1189,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) ) )
= $false )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1190,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1191,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1192,plain,
! [SV95: nat,SV51: nat] :
( ( ( ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1193,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( ~ ( SV52 @ ( suc @ ( sK7_SY165 @ SV96 @ SV52 ) ) ) )
= $false )
| ( ( SV52 @ zero_zero_nat )
= $true )
| ( ( SV52 @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1194,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( SV52 @ ( sK7_SY165 @ SV96 @ SV52 ) )
= $false )
| ( ( SV52 @ zero_zero_nat )
= $true )
| ( ( SV52 @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1195,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1196,plain,
! [SV53: nat] :
( ( ( SV53 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1197,plain,
! [SV53: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV53 ) )
= $false )
| ( ( SV53 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1198,plain,
! [SV53: nat] :
( ( ( ~ ( ( SV53 != zero_zero_nat ) ) )
= $false )
| ( ( SV53 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1199,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
= $false )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1200,plain,
! [SV97: nat,SV54: int] :
( ( ( ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1201,plain,
! [SV97: nat,SV54: int] :
( ( ( SV54 != zero_zero_int )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $true )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1202,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1203,plain,
! [SV98: nat,SV55: nat] :
( ( ( ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $false )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1204,plain,
! [SV98: nat,SV55: nat] :
( ( ( SV55 != zero_zero_nat )
= $true )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1205,plain,
! [SV99: nat > $o,SV57: nat,SV124: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SV124 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1206,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1207,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1208,plain,
! [SV102: nat,SV60: nat,SV118: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV118 ) )
= $true )
| ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1209,plain,
! [SV62: nat] :
( ( ( ~ ( ( SV62 != zero_zero_nat ) ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1210,plain,
! [SV62: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV62 ) )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1211,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1212,plain,
! [SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1213,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1214,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1215,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat ) )
= $true )
| ( ( ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1216,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( ~ ( SV68 @ ( sK9_SY183 @ SV106 @ SV68 ) ) )
= $false )
| ( ( SV68 @ SV106 )
= $true )
| ( ( SV68 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1217,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( SV68 @ ( suc @ ( sK9_SY183 @ SV106 @ SV68 ) ) )
= $false )
| ( ( SV68 @ SV106 )
= $true )
| ( ( SV68 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1218,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ( SV71 @ SV125 ) )
= $true )
| ( ( ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1219,plain,
! [SV75: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1220,plain,
! [SV75: nat] :
( ( ( ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1221,plain,
! [SV123: nat,SV75: nat] :
( ( ( SV75
= ( suc @ SV123 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1222,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ( ! [SY195: nat] : ( SV76 @ zero_zero_nat @ ( suc @ SY195 ) ) )
= $false )
| ( ( ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1223,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( ~ ( SV81 @ ( sK10_SY202 @ SV113 @ SV81 ) ) )
= $false )
| ( ( SV81 @ SV113 )
= $true )
| ( ( SV81 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1224,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( SV81 @ ( suc @ ( sK10_SY202 @ SV113 @ SV81 ) ) )
= $false )
| ( ( SV81 @ SV113 )
= $true )
| ( ( SV81 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1225,plain,
! [SV2: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV2 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1226,plain,
! [SV2: nat] :
( ( ( SV2 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1227,plain,
! [SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false )
| ( ( SV2 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1228,plain,
! [SV3: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV3 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1229,plain,
! [SV3: nat] :
( ( ( SV3 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1230,plain,
! [SV3: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $false )
| ( ( SV3 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1231,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno190918219poly_a @ SV82 )
= $true )
| ( ( polyno190918219poly_a @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1232,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $true )
| ( ( polyno190918219poly_a @ SV82 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1233,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno190918219poly_a @ SV82 )
= $true )
| ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1234,plain,
! [SV82: polyno727731844poly_a] :
( ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $true )
| ( ( polyno1372495879olyh_a @ SV82 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1235,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1236,plain,
! [SV83: nat,SV18: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1237,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1238,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1239,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) ) )
= $false )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1240,plain,
! [SV83: nat,SV18: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) ) )
= $false )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1241,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1242,plain,
! [SV27: nat,SV84: nat] :
( ( ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) )
= $true )
| ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1243,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
= $false )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1244,plain,
! [SV27: nat,SV84: nat] :
( ( ( ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1245,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
!= ( suc @ zero_zero_nat ) )
= $false )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1246,plain,
! [SV27: nat,SV84: nat] :
( ( ( ~ ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) ) )
= $false )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1247,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1248,plain,
! [SV85: nat,SV29: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1249,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1250,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1251,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) ) )
= $false )
| ( ( SV85 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1252,plain,
! [SV85: nat,SV29: nat] :
( ( ( ~ ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) ) )
= $false )
| ( ( SV85 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1253,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $true )
| ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1254,plain,
! [SV86: nat,SV30: nat] :
( ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $true )
| ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1255,plain,
! [SV86: nat,SV30: nat] :
( ( ( ( minus_minus_nat @ SV30 @ SV86 )
= zero_zero_nat )
= $true )
| ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1256,plain,
! [SV86: nat,SV30: nat] :
( ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $true )
| ( ( ord_less_eq_nat @ SV30 @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1257,plain,
! [SV87: nat,SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1258,plain,
! [SV35: nat,SV87: nat] :
( ( ( ord_less_nat @ SV87 @ SV35 )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1259,plain,
! [SV87: nat,SV35: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ SV35 @ SV87 ) )
= $true )
| ( ( ord_less_nat @ SV87 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1178]) ).
thf(1260,plain,
! [SV35: nat,SV87: nat] :
( ( ( ord_less_nat @ SV87 @ SV35 )
= $true )
| ( ( ord_less_nat @ SV87 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1261,plain,
! [SV41: nat,SV90: nat,SV114: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV90 )
| ( SV41 = SV114 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
= $false )
| ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1262,plain,
! [SV43: nat > $o,SV92: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( sK6_SY155 @ SV92 @ SV43 ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1263,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( ~ ~ ( SV43 @ ( sK6_SY155 @ SV92 @ SV43 ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1264,plain,
! [SV43: nat > $o,SV92: nat] :
( ( ( ~ ! [SY230: nat] :
~ ~ ( ~ ( ord_less_nat @ SY230 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SY230 ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1265,plain,
! [SV93: nat,SV46: nat,SV116: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV116 )
= $false )
| ( ( SV46 = SV116 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV46 )
= $false )
| ( ( ( power_power_nat @ SV46 @ ( suc @ SV93 ) )
= ( power_power_nat @ SV116 @ ( suc @ SV93 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1266,plain,
! [SV47: nat,SV94: nat,SV117: nat] :
( ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1267,plain,
! [SV50: nat] :
( ( ( SV50 != zero_zero_nat )
= $true )
| ( ( SV50 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1268,plain,
! [SV50: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $true )
| ( ( SV50 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1269,plain,
! [SV50: nat] :
( ( ( SV50 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1270,plain,
! [SV95: nat,SV51: nat] :
( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1271,plain,
! [SV95: nat,SV51: nat] :
( ( ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1272,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1273,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1274,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( ~ ~ ( ( SV51
!= ( suc @ SV126 ) )
| ~ ( ord_less_nat @ SV126 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1275,plain,
! [SV96: nat,SV52: nat > $o] :
( ( ( SV52 @ ( suc @ ( sK7_SY165 @ SV96 @ SV52 ) ) )
= $true )
| ( ( SV52 @ zero_zero_nat )
= $true )
| ( ( SV52 @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1276,plain,
! [SV53: nat] :
( ( ( SV53 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1277,plain,
! [SV53: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV53 )
= $true )
| ( ( SV53 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1278,plain,
! [SV53: nat] :
( ( ( SV53 != zero_zero_nat )
= $true )
| ( ( SV53 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1279,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1280,plain,
! [SV97: nat,SV54: int] :
( ( ( ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $true )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1281,plain,
! [SV97: nat,SV54: int] :
( ( ( SV54 = zero_zero_int )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $true )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1282,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1283,plain,
! [SV98: nat,SV55: nat] :
( ( ( ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $true )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1284,plain,
! [SV98: nat,SV55: nat] :
( ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1285,plain,
! [SV99: nat > $o,SV57: nat,SV124: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SV124 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1286,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1287,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1288,plain,
! [SV99: nat > $o,SV57: nat,SV127: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV127 @ SV57 )
| ~ ( SV99 @ ( suc @ SV127 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1289,plain,
! [SV102: nat,SV60: nat,SV118: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1290,plain,
! [SV62: nat] :
( ( ( SV62 != zero_zero_nat )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1291,plain,
! [SV62: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $true )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1292,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1293,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1294,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1295,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1296,plain,
! [SV106: nat,SV68: nat > $o] :
( ( ( SV68 @ ( sK9_SY183 @ SV106 @ SV68 ) )
= $true )
| ( ( SV68 @ SV106 )
= $true )
| ( ( SV68 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1297,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( SV71 @ SV125 )
= $false )
| ( ( ~ ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $true )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1298,plain,
! [SV75: nat] :
( ( ( ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1299,plain,
! [SV123: nat,SV75: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 )
| ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1300,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) )
| ( SV76 @ SV110 @ SV121 ) )
= $true )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1222]) ).
thf(1301,plain,
! [SV113: nat,SV81: nat > $o] :
( ( ( SV81 @ ( sK10_SY202 @ SV113 @ SV81 ) )
= $true )
| ( ( SV81 @ SV113 )
= $true )
| ( ( SV81 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1302,plain,
! [SV2: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1303,plain,
! [SV3: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1304,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $true )
| ( ( SV83 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1305,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1306,plain,
! [SV83: nat,SV18: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1307,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ SV18 ) @ SV83 ) )
= $true )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1239]) ).
thf(1308,plain,
! [SV83: nat,SV18: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
| ( SV83 = zero_zero_nat ) )
= $true )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1309,plain,
! [SV27: nat,SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $true )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1310,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1311,plain,
! [SV27: nat,SV84: nat] :
( ( ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) )
= $true )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1312,plain,
! [SV84: nat,SV27: nat] :
( ( ( ( power_power_nat @ SV27 @ SV84 )
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1313,plain,
! [SV27: nat,SV84: nat] :
( ( ( ( SV84 = zero_zero_nat )
| ( SV27
= ( suc @ zero_zero_nat ) ) )
= $true )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1314,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $true )
| ( ( SV85 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1315,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1316,plain,
! [SV85: nat,SV29: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1317,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ SV29 @ SV85 ) )
= $true )
| ( ( SV85 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1318,plain,
! [SV85: nat,SV29: nat] :
( ( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
| ( SV85 = zero_zero_nat ) )
= $true )
| ( ( SV85 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1319,plain,
! [SV114: nat,SV41: nat,SV90: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV90 ) )
= $true )
| ( ( SV41 = SV114 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
= $false )
| ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1320,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( ~ ( SV43 @ ( sK6_SY155 @ SV92 @ SV43 ) ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1321,plain,
! [SV43: nat > $o,SV92: nat] :
( ( ( ! [SY230: nat] :
~ ~ ( ~ ( ord_less_nat @ SY230 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SY230 ) ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1322,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ~ ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 = SV117 ) )
| ~ ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1266]) ).
thf(1323,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= ( SV94 = SV117 ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1266]) ).
thf(1324,plain,
! [SV50: nat] :
( ( ( SV50 = zero_zero_nat )
= $false )
| ( ( SV50 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1325,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1326,plain,
! [SV95: nat,SV51: nat] :
( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1327,plain,
! [SV95: nat,SV51: nat] :
( ( ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1328,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( ~ ( ( SV51
!= ( suc @ SV126 ) )
| ~ ( ord_less_nat @ SV126 @ SV95 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1329,plain,
! [SV53: nat] :
( ( ( SV53 = zero_zero_nat )
= $false )
| ( ( SV53 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1330,plain,
! [SV97: nat,SV54: int] :
( ( ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $false )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1331,plain,
! [SV54: int,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ~ ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1332,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $false )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1333,plain,
! [SV55: nat,SV98: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1334,plain,
! [SV99: nat > $o,SV57: nat,SV124: nat] :
( ( ( ~ ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1335,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1336,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1337,plain,
! [SV99: nat > $o,SV57: nat,SV127: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV127 @ SV57 )
| ~ ( SV99 @ ( suc @ SV127 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1338,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ( ord_less_eq_nat @ SV60 @ SV102 ) )
| ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1289]) ).
thf(1339,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1289]) ).
thf(1340,plain,
! [SV62: nat] :
( ( ( SV62 = zero_zero_nat )
= $false )
| ( ( SV62 = zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1341,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1342,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $false )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1343,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1344,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1345,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ! [SY188: nat] :
~ ~ ( ~ ~ ( SV71 @ SY188 )
| ~ ( SV71 @ ( suc @ SY188 ) ) ) )
= $false )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1346,plain,
! [SV75: nat] :
( ( ( SV75
!= ( suc @ ( sK12_SY191 @ SV75 ) ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1298]) ).
thf(1347,plain,
! [SV123: nat,SV75: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV75 ) )
= $false )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1348,plain,
! [SV123: nat,SV75: nat] :
( ( ( ~ ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1349,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ( ~ ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) ) )
= $true )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1350,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $true )
| ( ( SV83 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1351,plain,
! [SV83: nat,SV18: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV18 )
= $true )
| ( ( SV83 = zero_zero_nat )
= $true )
| ( ( SV83 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1352,plain,
! [SV27: nat,SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $true )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV84 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1353,plain,
! [SV27: nat,SV84: nat] :
( ( ( SV84 = zero_zero_nat )
= $true )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $true )
| ( ( SV27
= ( suc @ zero_zero_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1354,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $true )
| ( ( SV85 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1355,plain,
! [SV85: nat,SV29: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV29 )
= $true )
| ( ( SV85 = zero_zero_nat )
= $true )
| ( ( SV85 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1356,plain,
! [SV114: nat,SV41: nat,SV90: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV90 )
= $false )
| ( ( SV41 = SV114 )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV114 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV41 )
= $false )
| ( ( ( power_power_nat @ SV41 @ SV90 )
= ( power_power_nat @ SV114 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1357,plain,
! [SV92: nat,SV43: nat > $o] :
( ( ( SV43 @ ( sK6_SY155 @ SV92 @ SV43 ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1358,plain,
! [SV43: nat > $o,SV92: nat,SV128: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SV128 ) ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1359,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ~ ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 = SV117 ) ) )
= $true )
| ( ( ~ ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1360,plain,
! [SV95: nat,SV51: nat] :
( ( ( ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1361,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1362,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( ( SV51
!= ( suc @ SV126 ) )
| ~ ( ord_less_nat @ SV126 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1363,plain,
! [SV97: nat,SV54: int] :
( ( ( SV54 != zero_zero_int )
= $false )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1330]) ).
thf(1364,plain,
! [SV54: int,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $false )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1330]) ).
thf(1365,plain,
! [SV97: nat,SV54: int] :
( ( ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
| ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1366,plain,
! [SV98: nat,SV55: nat] :
( ( ( SV55 != zero_zero_nat )
= $false )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1367,plain,
! [SV55: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $false )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1368,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
| ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1369,plain,
! [SV99: nat > $o,SV57: nat,SV124: nat] :
( ( ( ~ ( ord_less_nat @ SV124 @ ( suc @ SV57 ) ) )
= $true )
| ( ( ~ ( SV99 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1370,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1371,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1372,plain,
! [SV99: nat > $o,SV57: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ SV127 @ SV57 )
| ~ ( SV99 @ ( suc @ SV127 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1373,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ~ ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1374,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1375,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1376,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1377,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1378,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
| ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1344]) ).
thf(1379,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ~ ( ~ ~ ( SV71 @ ( sK14_SY188 @ SV125 @ SV71 ) )
| ~ ( SV71 @ ( suc @ ( sK14_SY188 @ SV125 @ SV71 ) ) ) ) )
= $false )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1345]) ).
thf(1380,plain,
! [SV75: nat] :
( ( ( SV75
= ( suc @ ( sK12_SY191 @ SV75 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1381,plain,
! [SV123: nat,SV75: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV75 )
= $true )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1382,plain,
! [SV123: nat,SV75: nat] :
( ( ( ~ ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $true )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1383,plain,
! [SV121: nat,SV110: nat,SV76: nat > nat > $o] :
( ( ( ! [SY196: nat,SY197: nat] :
( ~ ( SV76 @ SY196 @ SY197 )
| ( SV76 @ ( suc @ SY196 ) @ ( suc @ SY197 ) ) ) )
= $false )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1384,plain,
! [SV43: nat > $o,SV92: nat,SV128: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SV128 ) ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1385,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 = SV117 ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1386,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ~ ( ( SV51
!= ( suc @ ( sK15_SY209 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK15_SY209 @ SV95 @ SV51 ) @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1360]) ).
thf(1387,plain,
! [SV95: nat,SV51: nat] :
( ( ( ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1388,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( SV51
!= ( suc @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_nat @ SV126 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1389,plain,
! [SV97: nat,SV54: int] :
( ( ( SV54 = zero_zero_int )
= $true )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1390,plain,
! [SV54: int,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $true )
| ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1391,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
!= zero_zero_int )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1392,plain,
! [SV97: nat,SV54: int] :
( ( ( ~ ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1393,plain,
! [SV98: nat,SV55: nat] :
( ( ( SV55 = zero_zero_nat )
= $true )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1394,plain,
! [SV55: nat,SV98: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $true )
| ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1395,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
!= zero_zero_nat )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1396,plain,
! [SV98: nat,SV55: nat] :
( ( ( ~ ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1397,plain,
! [SV99: nat > $o,SV57: nat,SV124: nat] :
( ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( ~ ( SV99 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1398,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK16_SY211 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK16_SY211 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1370]) ).
thf(1399,plain,
! [SV99: nat > $o,SV57: nat] :
( ( ( ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1400,plain,
! [SV99: nat > $o,SV57: nat,SV127: nat] :
( ( ( ~ ( ord_less_nat @ SV127 @ SV57 ) )
= $true )
| ( ( ~ ( SV99 @ ( suc @ SV127 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1401,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1402,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1374]) ).
thf(1403,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1404,plain,
! [SV104: nat > $o,SV65: nat,SV129: nat] :
( ( ( ~ ( ord_less_nat @ SV129 @ ( suc @ SV65 ) )
| ( SV104 @ SV129 ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1405,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1406,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1407,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1408,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ( ~ ~ ( SV71 @ ( sK14_SY188 @ SV125 @ SV71 ) )
| ~ ( SV71 @ ( suc @ ( sK14_SY188 @ SV125 @ SV71 ) ) ) ) )
= $true )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1409,plain,
! [SV123: nat,SV75: nat] :
( ( ( ! [SY191: nat] :
( SV75
!= ( suc @ SY191 ) ) )
= $false )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1410,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( ! [SY231: nat] :
( ~ ( SV76 @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) @ SY231 )
| ( SV76 @ ( suc @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) ) @ ( suc @ SY231 ) ) ) )
= $false )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1383]) ).
thf(1411,plain,
! [SV43: nat > $o,SV92: nat,SV128: nat] :
( ( ( ~ ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) )
| ~ ~ ( SV43 @ SV128 ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1412,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1413,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( SV94 = SV117 )
= $false )
| ( ( ~ ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) ) )
= $true )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1414,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ( SV51
!= ( suc @ ( sK15_SY209 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK15_SY209 @ SV95 @ SV51 ) @ SV95 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1415,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ~ ( ( SV51
!= ( suc @ ( sK18_SY209 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK18_SY209 @ SV95 @ SV51 ) @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1387]) ).
thf(1416,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ~ ( ord_less_nat @ SV126 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1417,plain,
! [SV97: nat,SV54: int] :
( ( ( ( power_power_int @ SV54 @ SV97 )
= zero_zero_int )
= $true )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1418,plain,
! [SV97: nat,SV54: int] :
( ( ( ~ ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) ) )
= $true )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1419,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( power_power_nat @ SV55 @ SV98 )
= zero_zero_nat )
= $true )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1420,plain,
! [SV98: nat,SV55: nat] :
( ( ( ~ ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) ) )
= $true )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1421,plain,
! [SV57: nat,SV124: nat,SV99: nat > $o] :
( ( ( SV99 @ SV124 )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1422,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK16_SY211 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK16_SY211 @ SV99 @ SV57 ) ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1423,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK19_SY212 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK19_SY212 @ SV99 @ SV57 ) ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1399]) ).
thf(1424,plain,
! [SV99: nat > $o,SV57: nat,SV127: nat] :
( ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( ~ ( SV99 @ ( suc @ SV127 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1425,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1426,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) ) )
= $true )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1427,plain,
! [SV104: nat > $o,SV65: nat,SV130: nat] :
( ( ( ~ ( ord_less_nat @ SV130 @ ( suc @ SV65 ) )
| ( SV104 @ SV130 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1428,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1429,plain,
! [SV104: nat > $o,SV65: nat,SV129: nat] :
( ( ( ~ ( ord_less_nat @ SV129 @ ( suc @ SV65 ) ) )
= $true )
| ( ( SV104 @ SV129 )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1430,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat ) )
= $false )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1431,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1405]) ).
thf(1432,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ~ ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1433,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1434,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ~ ( SV71 @ ( sK14_SY188 @ SV125 @ SV71 ) )
| ~ ( SV71 @ ( suc @ ( sK14_SY188 @ SV125 @ SV71 ) ) ) )
= $false )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1435,plain,
! [SV123: nat,SV75: nat] :
( ( ( SV75
!= ( suc @ ( sK20_SY191 @ SV123 @ SV75 ) ) )
= $false )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1409]) ).
thf(1436,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( ~ ( SV76 @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) @ ( sK21_SY231 @ SV110 @ SV121 @ SV76 ) )
| ( SV76 @ ( suc @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) ) @ ( suc @ ( sK21_SY231 @ SV110 @ SV121 @ SV76 ) ) ) )
= $false )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1410]) ).
thf(1437,plain,
! [SV43: nat > $o,SV92: nat,SV128: nat] :
( ( ( ~ ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) ) )
= $true )
| ( ( ~ ~ ( SV43 @ SV128 ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1438,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) )
= $false )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1439,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
| ( SV94 != SV117 ) )
= $false )
| ( ( SV94 = SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1440,plain,
! [SV95: nat,SV51: nat] :
( ( ( ( SV51
!= ( suc @ ( sK15_SY209 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK15_SY209 @ SV95 @ SV51 ) @ SV95 ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1441,plain,
! [SV95: nat,SV51: nat] :
( ( ( ~ ( ( SV51
!= ( suc @ ( sK18_SY209 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK18_SY209 @ SV95 @ SV51 ) @ SV95 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1442,plain,
! [SV51: nat,SV95: nat,SV126: nat] :
( ( ( ord_less_nat @ SV126 @ SV95 )
= $false )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1443,plain,
! [SV97: nat,SV54: int] :
( ( ( ( SV54 != zero_zero_int )
| ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1444,plain,
! [SV98: nat,SV55: nat] :
( ( ( ( SV55 != zero_zero_nat )
| ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1445,plain,
! [SV124: nat,SV99: nat > $o,SV57: nat] :
( ( ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1446,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK16_SY211 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK16_SY211 @ SV99 @ SV57 ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1447,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK19_SY212 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK19_SY212 @ SV99 @ SV57 ) ) ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1448,plain,
! [SV57: nat,SV127: nat,SV99: nat > $o] :
( ( ( SV99 @ ( suc @ SV127 ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( ~ ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1449,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $false )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1450,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
| ~ ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $false )
| ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1451,plain,
! [SV104: nat > $o,SV65: nat,SV130: nat] :
( ( ( ~ ( ord_less_nat @ SV130 @ ( suc @ SV65 ) ) )
= $true )
| ( ( SV104 @ SV130 )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1452,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1453,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1454,plain,
! [SV104: nat > $o,SV65: nat,SV129: nat] :
( ( ( ord_less_nat @ SV129 @ ( suc @ SV65 ) )
= $false )
| ( ( SV104 @ SV129 )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1455,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ zero_zero_nat )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1456,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1457,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) )
| ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1458,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1459,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1460,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ~ ( SV71 @ ( sK14_SY188 @ SV125 @ SV71 ) ) )
= $false )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1461,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ( SV71 @ ( suc @ ( sK14_SY188 @ SV125 @ SV71 ) ) ) )
= $false )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1462,plain,
! [SV123: nat,SV75: nat] :
( ( ( SV75
= ( suc @ ( sK20_SY191 @ SV123 @ SV75 ) ) )
= $true )
| ( ( SV75
= ( suc @ SV123 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1463,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( ~ ( SV76 @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) @ ( sK21_SY231 @ SV110 @ SV121 @ SV76 ) ) )
= $false )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1464,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( suc @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) ) @ ( suc @ ( sK21_SY231 @ SV110 @ SV121 @ SV76 ) ) )
= $false )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1465,plain,
! [SV43: nat > $o,SV92: nat,SV128: nat] :
( ( ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) )
= $false )
| ( ( ~ ~ ( SV43 @ SV128 ) )
= $true )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1466,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1467,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( SV94 != SV117 )
= $false )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1468,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( power_power_nat @ SV94 @ SV47 )
!= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( SV94 = SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1469,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( SV94 != SV117 )
= $false )
| ( ( SV94 = SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1470,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51
!= ( suc @ ( sK15_SY209 @ SV95 @ SV51 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1471,plain,
! [SV51: nat,SV95: nat] :
( ( ( ~ ( ord_less_nat @ ( sK15_SY209 @ SV95 @ SV51 ) @ SV95 ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1472,plain,
! [SV95: nat,SV51: nat] :
( ( ( ( SV51
!= ( suc @ ( sK18_SY209 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK18_SY209 @ SV95 @ SV51 ) @ SV95 ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1473,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
| ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $false )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1474,plain,
! [SV97: nat,SV54: int] :
( ( ( SV54 != zero_zero_int )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1475,plain,
! [SV54: int,SV97: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV97 ) )
= $false )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1476,plain,
! [SV98: nat,SV55: nat] :
( ( ( SV55 != zero_zero_nat )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1477,plain,
! [SV55: nat,SV98: nat] :
( ( ( ~ ( ord_less_nat @ zero_zero_nat @ SV98 ) )
= $false )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1478,plain,
! [SV124: nat,SV99: nat > $o,SV57: nat] :
( ( ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1479,plain,
! [SV124: nat,SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1480,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK16_SY211 @ SV99 @ SV57 ) @ ( suc @ SV57 ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1481,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( SV99 @ ( sK16_SY211 @ SV99 @ SV57 ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1482,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK19_SY212 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK19_SY212 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1483,plain,
! [SV127: nat,SV99: nat > $o,SV57: nat] :
( ( ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) )
| ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1484,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) ) )
= $false )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1485,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $false )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1486,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) ) )
= $false )
| ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1487,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ~ ( ord_less_eq_nat @ SV60 @ SV102 ) )
= $false )
| ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1488,plain,
! [SV104: nat > $o,SV65: nat,SV130: nat] :
( ( ( ord_less_nat @ SV130 @ ( suc @ SV65 ) )
= $false )
| ( ( SV104 @ SV130 )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1489,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1490,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1491,plain,
! [SV104: nat > $o,SV65: nat,SV131: nat] :
( ( ( ~ ( ord_less_nat @ SV131 @ SV65 )
| ( SV104 @ ( suc @ SV131 ) ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1492,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1493,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1494,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1495,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1496,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( ~ ( SV71 @ ( sK14_SY188 @ SV125 @ SV71 ) ) )
= $true )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1497,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( SV71 @ ( suc @ ( sK14_SY188 @ SV125 @ SV71 ) ) )
= $true )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1498,plain,
! [SV110: nat,SV121: nat,SV76: nat > nat > $o] :
( ( ( SV76 @ ( sK17_SY196 @ SV121 @ SV110 @ SV76 ) @ ( sK21_SY231 @ SV110 @ SV121 @ SV76 ) )
= $true )
| ( ( SV76 @ SV110 @ SV121 )
= $true )
| ( ( SV76 @ zero_zero_nat @ ( suc @ ( sK11_SY195 @ SV121 @ SV110 @ SV76 ) ) )
= $false )
| ( ( SV76 @ ( sK5_SY194 @ SV121 @ SV110 @ SV76 ) @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1499,plain,
! [SV92: nat,SV128: nat,SV43: nat > $o] :
( ( ( ~ ( SV43 @ SV128 ) )
= $false )
| ( ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1500,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $true )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1501,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( SV94 = SV117 )
= $true )
| ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1502,plain,
! [SV117: nat,SV47: nat,SV94: nat] :
( ( ( ( power_power_nat @ SV94 @ SV47 )
= ( power_power_nat @ SV117 @ SV47 ) )
= $true )
| ( ( SV94 = SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1503,plain,
! [SV47: nat,SV117: nat,SV94: nat] :
( ( ( SV94 = SV117 )
= $true )
| ( ( SV94 = SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV117 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV94 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1504,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51
= ( suc @ ( sK15_SY209 @ SV95 @ SV51 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1505,plain,
! [SV51: nat,SV95: nat] :
( ( ( ord_less_nat @ ( sK15_SY209 @ SV95 @ SV51 ) @ SV95 )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1506,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51
!= ( suc @ ( sK18_SY209 @ SV95 @ SV51 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1507,plain,
! [SV51: nat,SV95: nat] :
( ( ( ~ ( ord_less_nat @ ( sK18_SY209 @ SV95 @ SV51 ) @ SV95 ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1508,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( ~ ( ord_less_nat @ SV51 @ ( suc @ SV95 ) ) )
= $false )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1509,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( ~ ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) ) )
= $false )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1510,plain,
! [SV97: nat,SV54: int] :
( ( ( SV54 = zero_zero_int )
= $true )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1474]) ).
thf(1511,plain,
! [SV54: int,SV97: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $true )
| ( ( SV54 = zero_zero_int )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1512,plain,
! [SV98: nat,SV55: nat] :
( ( ( SV55 = zero_zero_nat )
= $true )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1513,plain,
! [SV55: nat,SV98: nat] :
( ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $true )
| ( ( SV55 = zero_zero_nat )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1514,plain,
! [SV124: nat,SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1515,plain,
! [SV124: nat,SV57: nat,SV99: nat > $o] :
( ( ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1516,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ord_less_nat @ ( sK16_SY211 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1517,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( SV99 @ ( sK16_SY211 @ SV99 @ SV57 ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1518,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ord_less_nat @ ( sK19_SY212 @ SV99 @ SV57 ) @ SV57 ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1519,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ~ ( SV99 @ ( suc @ ( sK19_SY212 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1520,plain,
! [SV127: nat,SV99: nat > $o,SV57: nat] :
( ( ( ~ ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1521,plain,
! [SV127: nat,SV57: nat,SV99: nat > $o] :
( ( ( ~ ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1522,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1523,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $true )
| ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1524,plain,
! [SV102: nat,SV118: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ ( power_power_nat @ SV60 @ SV118 ) @ ( power_power_nat @ SV102 @ SV118 ) )
= $true )
| ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1525,plain,
! [SV118: nat,SV102: nat,SV60: nat] :
( ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $true )
| ( ( ord_less_eq_nat @ SV60 @ SV102 )
= $false )
| ( ( ord_less_nat @ zero_zero_nat @ SV118 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV102 )
= $false )
| ( ( ord_less_eq_nat @ zero_zero_nat @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1526,plain,
! [SV104: nat > $o,SV65: nat,SV132: nat] :
( ( ( ~ ( ord_less_nat @ SV132 @ SV65 )
| ( SV104 @ ( suc @ SV132 ) ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1527,plain,
! [SV104: nat > $o,SV65: nat,SV131: nat] :
( ( ( ~ ( ord_less_nat @ SV131 @ SV65 ) )
= $true )
| ( ( SV104 @ ( suc @ SV131 ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1528,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY214: nat] :
( ~ ( ord_less_nat @ SY214 @ ( suc @ SV65 ) )
| ( SV104 @ SY214 ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1529,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1530,plain,
! [SV104: nat > $o,SV65: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV65 ) )
| ( SV104 @ SV133 ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1531,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1532,plain,
! [SV125: nat,SV71: nat > $o] :
( ( ( SV71 @ ( sK14_SY188 @ SV125 @ SV71 ) )
= $false )
| ( ( SV71 @ SV125 )
= $false )
| ( ( SV71 @ zero_zero_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1533,plain,
! [SV92: nat,SV128: nat,SV43: nat > $o] :
( ( ( SV43 @ SV128 )
= $true )
| ( ( ord_less_nat @ SV128 @ ( sK6_SY155 @ SV92 @ SV43 ) )
= $false )
| ( ( SV43 @ SV92 )
= $true )
| ( ( SV43 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1534,plain,
! [SV95: nat,SV51: nat] :
( ( ( SV51
= ( suc @ ( sK18_SY209 @ SV95 @ SV51 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1535,plain,
! [SV51: nat,SV95: nat] :
( ( ( ord_less_nat @ ( sK18_SY209 @ SV95 @ SV51 ) @ SV95 )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51 = zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1536,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( ord_less_nat @ SV51 @ ( suc @ SV95 ) )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1537,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( ( SV51 = zero_zero_nat )
| ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1538,plain,
! [SV124: nat,SV99: nat > $o,SV57: nat] :
( ( ( ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1539,plain,
! [SV124: nat,SV57: nat,SV99: nat > $o] :
( ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1540,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( ord_less_nat @ ( sK19_SY212 @ SV99 @ SV57 ) @ SV57 )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1541,plain,
! [SV57: nat,SV99: nat > $o] :
( ( ( SV99 @ ( suc @ ( sK19_SY212 @ SV99 @ SV57 ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1519]) ).
thf(1542,plain,
! [SV127: nat,SV99: nat > $o,SV57: nat] :
( ( ( ~ ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1543,plain,
! [SV127: nat,SV57: nat,SV99: nat > $o] :
( ( ( ( SV99 @ zero_zero_nat )
| ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1544,plain,
! [SV104: nat > $o,SV65: nat,SV132: nat] :
( ( ( ~ ( ord_less_nat @ SV132 @ SV65 ) )
= $true )
| ( ( SV104 @ ( suc @ SV132 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1545,plain,
! [SV104: nat > $o,SV65: nat,SV131: nat] :
( ( ( ord_less_nat @ SV131 @ SV65 )
= $false )
| ( ( SV104 @ ( suc @ SV131 ) )
= $true )
| ( ( SV104 @ ( sK8_SY214 @ SV104 @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1546,plain,
! [SV104: nat > $o,SV65: nat,SV134: nat] :
( ( ( ~ ( ord_less_nat @ SV134 @ ( suc @ SV65 ) )
| ( SV104 @ SV134 ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1547,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat )
| ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1548,plain,
! [SV104: nat > $o,SV65: nat,SV133: nat] :
( ( ( ~ ( ord_less_nat @ SV133 @ ( suc @ SV65 ) ) )
= $true )
| ( ( SV104 @ SV133 )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1549,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1550,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1551,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( SV51 = zero_zero_nat )
= $true )
| ( ( ~ ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1552,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1538]) ).
thf(1553,plain,
! [SV124: nat,SV99: nat > $o,SV57: nat] :
( ( ( ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1554,plain,
! [SV127: nat,SV99: nat > $o,SV57: nat] :
( ( ( ! [SY211: nat] :
~ ~ ( ~ ( ord_less_nat @ SY211 @ ( suc @ SV57 ) )
| ~ ( SV99 @ SY211 ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1555,plain,
! [SV127: nat,SV57: nat,SV99: nat > $o] :
( ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ~ ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1556,plain,
! [SV104: nat > $o,SV65: nat,SV132: nat] :
( ( ( ord_less_nat @ SV132 @ SV65 )
= $false )
| ( ( SV104 @ ( suc @ SV132 ) )
= $true )
| ( ( ord_less_nat @ ( sK8_SY214 @ SV104 @ SV65 ) @ ( suc @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1557,plain,
! [SV104: nat > $o,SV65: nat,SV134: nat] :
( ( ( ~ ( ord_less_nat @ SV134 @ ( suc @ SV65 ) ) )
= $true )
| ( ( SV104 @ SV134 )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1558,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( ~ ( SV104 @ zero_zero_nat ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1559,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ~ ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $false )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1560,plain,
! [SV104: nat > $o,SV65: nat,SV133: nat] :
( ( ( ord_less_nat @ SV133 @ ( suc @ SV65 ) )
= $false )
| ( ( SV104 @ SV133 )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1561,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ zero_zero_nat )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1562,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1563,plain,
! [SV126: nat,SV95: nat,SV51: nat] :
( ( ( ! [SY209: nat] :
~ ~ ( ( SV51
!= ( suc @ SY209 ) )
| ~ ( ord_less_nat @ SY209 @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1564,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1565,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1553]) ).
thf(1566,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1554]) ).
thf(1567,plain,
! [SV127: nat,SV99: nat > $o,SV57: nat] :
( ( ( ! [SY212: nat] :
~ ~ ( ~ ( ord_less_nat @ SY212 @ SV57 )
| ~ ( SV99 @ ( suc @ SY212 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1568,plain,
! [SV104: nat > $o,SV65: nat,SV134: nat] :
( ( ( ord_less_nat @ SV134 @ ( suc @ SV65 ) )
= $false )
| ( ( SV104 @ SV134 )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1569,plain,
! [SV65: nat,SV104: nat > $o] :
( ( ( SV104 @ zero_zero_nat )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1570,plain,
! [SV104: nat > $o,SV65: nat] :
( ( ( ! [SY215: nat] :
( ~ ( ord_less_nat @ SY215 @ SV65 )
| ( SV104 @ ( suc @ SY215 ) ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1571,plain,
! [SV104: nat > $o,SV65: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ SV135 @ SV65 )
| ( SV104 @ ( suc @ SV135 ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1572,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( ~ ~ ( ( SV51
!= ( suc @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) @ SV95 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1563]) ).
thf(1573,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ( ord_less_nat @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1574,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) ) ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1575,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) ) ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1576,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ~ ( ~ ( ord_less_nat @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1567]) ).
thf(1577,plain,
! [SV104: nat > $o,SV65: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ SV136 @ SV65 )
| ( SV104 @ ( suc @ SV136 ) ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1578,plain,
! [SV104: nat > $o,SV65: nat,SV135: nat] :
( ( ( ~ ( ord_less_nat @ SV135 @ SV65 ) )
= $true )
| ( ( SV104 @ ( suc @ SV135 ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1579,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( ~ ( ( SV51
!= ( suc @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) @ SV95 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1580,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ( ord_less_nat @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) @ ( suc @ SV57 ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1581,plain,
! [SV57: nat,SV124: nat,SV99: nat > $o] :
( ( ( ~ ( SV99 @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) ) )
= $false )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1582,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ( ord_less_nat @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1583,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
| ~ ( SV99 @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1584,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ( ~ ( ord_less_nat @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) ) ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1585,plain,
! [SV104: nat > $o,SV65: nat,SV136: nat] :
( ( ( ~ ( ord_less_nat @ SV136 @ SV65 ) )
= $true )
| ( ( SV104 @ ( suc @ SV136 ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1586,plain,
! [SV104: nat > $o,SV65: nat,SV135: nat] :
( ( ( ord_less_nat @ SV135 @ SV65 )
= $false )
| ( ( SV104 @ ( suc @ SV135 ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( SV104 @ ( suc @ ( sK13_SY215 @ SV104 @ SV65 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1587,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( ( SV51
!= ( suc @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) ) )
| ~ ( ord_less_nat @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) @ SV95 ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1588,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ord_less_nat @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1589,plain,
! [SV57: nat,SV124: nat,SV99: nat > $o] :
( ( ( SV99 @ ( sK22_SY211 @ SV124 @ SV99 @ SV57 ) )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1590,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ~ ( ord_less_nat @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) @ SV57 ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1591,plain,
! [SV57: nat,SV124: nat,SV99: nat > $o] :
( ( ( ~ ( SV99 @ ( suc @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1582]) ).
thf(1592,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) @ ( suc @ SV57 ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1593,plain,
! [SV57: nat,SV127: nat,SV99: nat > $o] :
( ( ( ~ ( SV99 @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) ) )
= $false )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1594,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) @ SV57 )
| ~ ( SV99 @ ( suc @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1595,plain,
! [SV104: nat > $o,SV65: nat,SV136: nat] :
( ( ( ord_less_nat @ SV136 @ SV65 )
= $false )
| ( ( SV104 @ ( suc @ SV136 ) )
= $true )
| ( ( SV104 @ zero_zero_nat )
= $false )
| ( ( ord_less_nat @ ( sK13_SY215 @ SV104 @ SV65 ) @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1596,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( SV51
!= ( suc @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1597,plain,
! [SV51: nat,SV95: nat,SV126: nat] :
( ( ( ~ ( ord_less_nat @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) @ SV95 ) )
= $false )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1598,plain,
! [SV57: nat,SV99: nat > $o,SV124: nat] :
( ( ( ord_less_nat @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) @ SV57 )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1599,plain,
! [SV57: nat,SV124: nat,SV99: nat > $o] :
( ( ( SV99 @ ( suc @ ( sK23_SY212 @ SV124 @ SV99 @ SV57 ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV124 @ ( suc @ SV57 ) )
= $false )
| ( ( SV99 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1600,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ord_less_nat @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) @ ( suc @ SV57 ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1601,plain,
! [SV57: nat,SV127: nat,SV99: nat > $o] :
( ( ( SV99 @ ( sK24_SY211 @ SV127 @ SV99 @ SV57 ) )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1602,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ~ ( ord_less_nat @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) @ SV57 ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1603,plain,
! [SV57: nat,SV127: nat,SV99: nat > $o] :
( ( ( ~ ( SV99 @ ( suc @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) ) ) )
= $false )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1594]) ).
thf(1604,plain,
! [SV95: nat,SV126: nat,SV51: nat] :
( ( ( SV51
= ( suc @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) ) )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1605,plain,
! [SV51: nat,SV95: nat,SV126: nat] :
( ( ( ord_less_nat @ ( sK25_SY209 @ SV126 @ SV95 @ SV51 ) @ SV95 )
= $true )
| ( ( SV51 = zero_zero_nat )
= $true )
| ( ( SV51
= ( suc @ SV126 ) )
= $false )
| ( ( ord_less_nat @ SV126 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1597]) ).
thf(1606,plain,
! [SV57: nat,SV99: nat > $o,SV127: nat] :
( ( ( ord_less_nat @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) @ SV57 )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1607,plain,
! [SV57: nat,SV127: nat,SV99: nat > $o] :
( ( ( SV99 @ ( suc @ ( sK26_SY212 @ SV127 @ SV99 @ SV57 ) ) )
= $true )
| ( ( SV99 @ zero_zero_nat )
= $true )
| ( ( ord_less_nat @ SV127 @ SV57 )
= $false )
| ( ( SV99 @ ( suc @ SV127 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1608,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[443,1607,1606,1605,1604,1601,1600,1599,1598,1595,1589,1588,1586,1569,1568,1561,1560,1556,1545,1541,1540,1536,1535,1534,1533,1532,1525,1524,1523,1522,1517,1516,1513,1512,1511,1510,1505,1504,1503,1502,1501,1500,1498,1497,1489,1488,1464,1462,1455,1454,1419,1417,1394,1393,1390,1389,1381,1380,1357,1356,1355,1354,1353,1352,1351,1350,1340,1339,1329,1326,1324,1323,1317,1315,1314,1312,1310,1309,1307,1305,1304,1303,1302,1301,1296,1292,1291,1282,1279,1277,1276,1275,1270,1269,1268,1265,1262,1260,1259,1258,1257,1256,1255,1254,1253,1247,1241,1235,1234,1233,1232,1231,1230,1229,1227,1226,1224,1219,1217,1212,1195,1194,1188,1163,1162,1161,1160,1159,1158,1157,1156,1155,1154,1153,1152,1147,1146,1145,1144,1143,1142,1141,1140,1139,1138,1137,1136,1135,1134,1133,1132,1131,1130,1129,1128,1127,1126,1125,1124,1119,1118,1117,1116,1115,1111,1106,1101,1099,1097,1087,1070,1068,999,969,924,916,915,866,864,853,851,832,831,799,796,790,787,785,781,769,767,765,763,758,750,743,739,736,729,725,715,711,709,708,704,697,692,690,688,685,684,682,680,678,676,674,671,670,668,667,666,665,663,661,615,614,612,611,610,609,606,604,603,602,600,599,594,587,585,530,468,467,466,444]) ).
thf(1609,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.21 % Computer : n005.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Oct 6 11:18:29 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.86/2.42 ..
% 11.86/2.42
% 11.86/2.42 No.of.Axioms: 88
% 11.86/2.42
% 11.86/2.42 Length.of.Defs: 0
% 11.86/2.42
% 11.86/2.42 Contains.Choice.Funs: false
% 11.86/2.42 ...............................
% 11.86/2.42
% 11.86/2.42 ********************************
% 11.86/2.42 * All subproblems solved! *
% 11.86/2.42 ********************************
% 11.86/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:88,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1608,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.86/2.42
% 11.86/2.42 %**** Beginning of derivation protocol ****
% 11.86/2.42 % SZS output start CNFRefutation
% See solution above
% 11.86/2.43
% 11.86/2.43 %**** End of derivation protocol ****
% 11.86/2.43 %**** no. of clauses in derivation: 1347 ****
% 11.86/2.43 %**** clause counter: 1608 ****
% 11.86/2.43
% 11.86/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:88,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1608,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------